text:
Godeta  – gaun wikas samiti w środkowej części Nepalu  w strefie Dźanakpur w dystrykcie Sarlahi. Według nepalskiego spisu powszechnego z 2001 roku liczył on 863 gospodarstw domowych i 5422 mieszkańców (2609 kobiet i 2813 mężczyzn).

Przypisy

Godeta

redpajama_set_name: RedPajamaWikipedia


text:
Gábor Vincze (born 7 September 1976) is a Hungarian retired football player. During his career he had a spell at Livingston in Scotland where he scored once against Rangers at Ibrox.

References

External links
 Vincze Gábor at HLSZ.hu-n

1976 births
Living people
Hungarian footballers
Hungary international footballers
Hungarian expatriate footballers
Ferencvárosi TC footballers
Debreceni VSC players
Győri ETO FC players
Livingston F.C. players
Ethnikos Achna FC players
Budapest Honvéd FC players
Expatriate footballers in Scotland
Expatriate footballers in Cyprus
Scottish Premier League players
Cypriot First Division players
Association football midfielders
Hungarian expatriate sportspeople in Scotland
People from Ózd
Sportspeople from Borsod-Abaúj-Zemplén County


Ah, the much anticipated inaugural blog post...much anticipated by me, anyhow. I've been excited to get started for months now on this page, and, well, here we go.
I have written for Suite101 and Examiner as a food writer. While I had great experiences on both sites, I look forward to doing this my way now, without pesky editors telling me how they prefer it done. I intend to share my love of cooking, baking, and food, in general, with anyone who is willing to read.
I am addicted to the ooohing and awwwing that comes with serving up something great to eat. That addiction started when I was a little girl and an eager assistant cook and baker to my mother, who as a mother of five children, stayed pretty busy. When I would serve anything, and I mean anything, to my father he would respond as if I had just served him sunshine on a plate. I have been hooked on making food and watching it recharge people's moods, and distributing a little guilty pleasure at times, ever since.
I am an avid home cook and it is safe to describe me as a wanna-be-chef. I have a huge recipe collection that I began putting together over 15 years ago and I am still adding to it. At times, I've wondered what I would ever do with all of those recipes...I'm fairly certain this blog is my solution.


"You've Lost That Lovin' Feelin'," "On Broadway," "(You're My) Soul and Inspiration": These are just a few of the classic songs that husband and wife team Barry Mann and Cynthia Weil has written. The wildly successful partnership has spanned nearly every genre of popular music, from pop to rock to r&b to country, with film and stage work also figuring heavily in the mix.
Such versatility is nothing less than astounding. While many of their contemporaries have focused on writing only pop songs or only r&b tunes, Mann and Weil have consistently proven themselves adept at working in a wide range of styles, often working with other songwriters either alone or as a team.
The recognition that they have received is extraordinary in itself: Mann and Weil have collected myriad accolades from BMI, including 108 Pop, Country and R&B Awards and 76 "Million-Air" Awards, denoting airplay of 1 million or more. "You've Lost That Lovin' Feelin'" is the most performed song in BMI's repertoire and is the first song ever to achieve 8 million performances.
In addition, the twosome received the first Lifetime Achievement Award from the National Academy of Songwriters, The Clooney Foundation's Award for Legendary Song Composition, and has been inducted into the Songwriters Hall of Fame.
The Mann & Weil story has a humble beginning. While still a teenager, Mann gave up studying architecture to become a full-time songwriter. After penning "She Say (Oom Dooby Dom)," a hit for the Diamonds, Mann joined music publisher Aldon Music as a staff writer. There he co-wrote such hits as "Footsteps" by Steve Lawrence, "I Love How You Love Me" by The Paris Sisters," and "Patches" by Dicky Lee. A talented singer in his own right, in 1961 Mann recorded the hit single "Who Put the Bomp (In the Bomp, Bomp, Bomp)," co-written by Gerry Goffin.
Weil began her career as an actress and dancer, but, encouraged by famed composer Frank Loesser, soon began pursuing songwriting as a career. Before long she, too, found herself at Aldon, where a professional relationship soon began with Mann. This was the famed "Brill Building" era, during which the pair competed and sometimes collaborated with such other talents as Goffin, Carole King, Jerry Lieber & Mike Stoller (with whom they wrote "On Broadway") and Phil Spector ("Lovin' Feelin'").
Songwriting was only one of Mann and Weil's collaborations, however; they married during their stay at Aldon. Professionally, as the partnership deepened and evolved, Mann would take care of the music while Weil wrote the lyrics. Weil's savvy extended well beyond the routine love songs that marked the era, and she is widely credited with helping to bring a political consciousness to the Brill Building style via such cornerstone works as "On Broadway" and "Uptown." The increasing intensity of their work became even more evident with such songs as "Kicks," a top 10 hit for Paul Revere & the Raiders, which examined the pitfalls of drug use, and "We Gotta Get Out of This Place," popularized by the Animals, which served as a desperate anthem for both Vietnam War soldiers and protesters.
Moving into the '70s, '80s and '90s, Mann & Weil were instrumental in crossing Dolly Parton over from country to pop ("Here You Come Again"), introducing James Ingram ("Just Once"), and reinvigorating the careers of Aaron Neville (the Grammy-nominated "Don't Know Much") and Sergio Mendes ("Never Gonna Let You Go"). During this period the pair also wrote with teen idols Hanson the hit ballad "I Will Come to You."
Hits have also consistently been scored with other tunesmiths: Weil wrote "Running with the Night" with Lionel Richie, "Through the Fire" with David Foster and Tom Keane, "He's So Shy" with Tom Snow and "Wrong Again," a number one country hit for Martina McBride, with Tommy Lee James. Mann has collaborated with such acts as Leo Sayer ("How Much Love"), Dan Hill ("Sometimes When We Touch") and Curtis Stigers ("Never Saw a Miracle").
The team has also made its mark in the film world, winning (with James Horner) a pair of Grammys, an Oscar nomination and a Golden Globe nomination for "Somewhere Out There" from An American Tail, receiving a Grammy nomination (with Horner) for "Whatever You Imagine" from The Pagemaster, and writing the song score for Muppet Treasure Island. In addition, Weil provided the Christmas carols (again with Horner) for the big-screen version of How the Grinch Stole Christmas and wrote the song "For Always" with John Williams for the A.I. soundtrack album.
Even after their many successes over the years, the team is hardly slowing down: In addition to songwriting, Mann and Weil are currently working on two Broadway projects: one based on their amazing catalog of songs, and Mask, an original rock musical based on the 1985 film.
Obviously, it is impossible to consider popular songwriting in the second half of the past century (and beyond) without including the landmark work of this phenomenal duo. Maintaining popular and critical success for such an extended time - and continuing to diligently hone their craft - Barry Mann and Cynthia Weil are, simply put, a songwriting team for the ages.


Prostate Cancer Foundation (PCF), a nonprofit organization which remains steadfast in its commitment to identify and fund groundbreaking cancer research programs to save the lives of millions, hosted its annual gala at the Parrish Art Museum in Water Mill, NY on Saturday, August 27, 2016. The event's Challenge Research Award raised over $3.5 million in support of the foundation's work.
Couture fashion designer Jackie Rogers presented her 2016 collection for all seasons at a private residence in Southampton, NY on Friday, August 26th. Guests viewed the latest from the Jackie Rogers Collection including dresses, jackets and separates. Pieces from the collection were on sale, and 20% of proceeds from this presentation were donated to the Southampton Fresh Air Home. The Home is a residential camp for physically challenged youth offering summer and year-round programs focused on recreation, education and independence.
Resident Magazine and Chelsea Station celebrated Jean Shafiroff, Philanthropist & Author of Successful Philanthropy: How To Make a Life by What You Give, on the cover of Resident Magazine's August Hamptons 2016 issue. The event, which took place on Wednesday, August 24th, 2016, was hosted by Publisher Michael Travin, Associate Publisher Melissa Kassis, and Editor-In-Chief Hillary Latos, at chic restaurant & bar Chelsea Station.
The Michael Bolton Charities held "An Evening Under the Stars" fundraising dinner and auction in Bridgehampton, NY on Saturday, August 20th, 2016. This year's honorees, receiving the Michael Bolton Lifetime Achievement Award, were Joe and Ali Torre of The Joe Torre Safe At Home Foundation for their commitment to ending domestic violence. The intimate evening, benefitting The Michael Bolton Charities, was produced by celebrity event planner Larry Scott of Lawrence Scott Events.
Luxury Mexican resort Mayakoba Residences' Managing Director Carlos Orozco hosted a private dinner party on Thursday, August 18th, 2016, featuring an extravagant La Ceiba Dinner and a special tasting of ultra-premium tequila Clase Azul. The sumptuous dinner was prepared by Executive Chef of the award-winning Rosewood Mayakoba, Juan Pablo Loza, along with Union Cantina's Executive Chef Scott Kampf. Guests were treated to an extraordinary 8 course authentic Mayan tasting menu, replicating a dining experience that is exclusive to guests of Rosewood Mayakoba resort, located in the idyllic Riviera Maya. The event was coordinated by the leading Sroka Worldwide marketing team, headed by industry veteran and company founder Neal Sroka.
The MOMS Denise Albert and Melissa Musen Gerstein along with New York Family Magazine hosted a Cover Party and a Back To School Special on SiriusXM on Tuesday, August 16th, 2016. The event was sponsored by: America's number one Greek yogurt Chobani Greek Yogurt, the world's largest submarine sandwich chain Subway, global underwear and casualwear company Fruit of the Loom, children's clothing and community giving company Kidbox and interactive music program Baby DJ School.
The East Hampton Library hosted their 12th Annual Authors Night on August 13th, 2016 with proceeds going to the advancement of the library. The premiere literary event brought together 100 distinguished authors with over 2,500 book lovers on the Maidstone Lane field in the East Hampton Village. Prominent philanthropist and author, Jean Shafiroff, was present to sign her debut book, Successful Philanthropy: How to Make a Life by What You Give – a guide to modern philanthropy.


text:
title: Gaussian processes
layout: post
comments: True
author: "Martin Krasser"
header-img: "img/distributed.png"
---

[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/krasserm/bayesian-machine-learning/blob/dev/gaussian-processes/gaussian_processes.ipynb)

*Sources:*
- *[Notebook](https://nbviewer.jupyter.org/github/krasserm/bayesian-machine-learning/blob/dev/gaussian-processes/gaussian_processes.ipynb)*
- *[Repository](https://github.com/krasserm/bayesian-machine-learning)*

*Series:*
- *Gaussian processes (this article)*
- *[Gaussian processes for classification](/2020/11/04/gaussian-processes-classification/)*
- *[Sparse Gaussian processes](/2020/12/12/gaussian-processes-sparse/)*

## Introduction

In supervised learning, we often use parametric models $p(\mathbf{y} \lvert \mathbf{X},\boldsymbol\theta)$ to explain data and infer optimal values of parameter $\boldsymbol\theta$ via [maximum likelihood](https://en.wikipedia.org/wiki/Maximum_likelihood_estimation) or [maximum a posteriori](https://de.wikipedia.org/wiki/Maximum_a_posteriori) estimation. If needed we can also infer a full [posterior distribution](https://en.wikipedia.org/wiki/Posterior_probability) $p(\boldsymbol\theta \lvert \mathbf{X},\mathbf{y})$ instead of a point estimate $\boldsymbol{\hat\theta}$. With increasing data complexity, models with a higher number of parameters are usually needed to explain data reasonably well. Methods that use models with a fixed number of parameters are called parametric methods.

In non-parametric methods, on the other hand, the number of parameters depend on the dataset size. For example, in [Nadaraya-Watson kernel regression](https://en.wikipedia.org/wiki/Kernel_regression), a weight $w_i$ is assigned to each observed target $y_i$ and for predicting the target value at a new point $\mathbf{x}$ a weighted average is computed:

$$f(\mathbf{x}) = \sum_{i=1}^{N}w_i(\mathbf{x})y_i$$

$$w_i(\mathbf{x}) = \frac{\kappa(\mathbf{x}, \mathbf{x}_{i})}{\sum_{i'=1}^{N}\kappa(\mathbf{x}, \mathbf{x}_{i'})}$$

Observations that are closer to $\mathbf{x}$ have a higher weight than observations that are further away. Weights are computed from $\mathbf{x}$ and observed $\mathbf{x}_i$ with a kernel $\kappa$. A special case is k-nearest neighbors (KNN) where the $k$ closest observations have a weight $1/k$, and all others have weight $0$. Non-parametric methods often need to process all training data for prediction and are therefore slower at inference time than parametric methods. On the other hand, training is usually faster as non-parametric models only need to remember training data.

Another example of non-parametric methods are [Gaussian processes](https://en.wikipedia.org/wiki/Gaussian_process) (GPs). Instead of inferring a distribution over the parameters of a parametric function Gaussian processes can be used to infer a distribution over functions directly. A Gaussian process defines a prior over functions. After having observed some function values it can be converted into a posterior over functions. Inference of continuous function values in this context is known as GP regression but GPs can also be used for [classification](/2020/11/04/gaussian-processes-classification/).

A Gaussian process is a [random process](https://en.wikipedia.org/wiki/Stochastic_process) where any point $\mathbf{x} \in \mathbb{R}^d$ is assigned a random variable $f(\mathbf{x})$ and where the joint distribution of a finite number of these variables $p(f(\mathbf{x}_1),...,f(\mathbf{x}_N))$ is itself Gaussian:

$$p(\mathbf{f} \lvert \mathbf{X}) = \mathcal{N}(\mathbf{f} \lvert \boldsymbol\mu, \mathbf{K})\tag{1}\label{eq1}$$

In Equation $(1)$, $\mathbf{f} = (f(\mathbf{x}\_1),...,f(\mathbf{x}\_N))$, $\boldsymbol\mu = (m(\mathbf{x}\_1),...,m(\mathbf{x}\_N))$ and $K\_{ij} = \kappa(\mathbf{x}\_i,\mathbf{x}\_j)$. $m$ is the mean function and it is common to use $m(\mathbf{x}) = 0$ as GPs are flexible enough to model the mean arbitrarily well. $\kappa$ is a positive definite *kernel function* or *covariance function*. Thus, a Gaussian process is a distribution over functions whose shape (smoothness, ...) is defined by $\mathbf{K}$. If points $\mathbf{x}_i$ and $\mathbf{x}_j$ are considered to be similar by the kernel the function values at these points, $f(\mathbf{x}_i)$ and $f(\mathbf{x}_j)$, can be expected to be similar too.

Given a training dataset with noise-free function values $\mathbf{f}$ at inputs $\mathbf{X}$, a GP prior can be converted into a GP posterior $p(\mathbf{f}\_* \lvert \mathbf{X}\_*,\mathbf{X},\mathbf{f})$ which can then be used to make predictions $\mathbf{f}\_\*$ at new inputs $\mathbf{X}\_\*$. By definition of a GP, the joint distribution of observed values $\mathbf{f}$ and predictions $\mathbf{f}\_\*$ is again a Gaussian which can be partitioned into

$$
\begin{pmatrix}\mathbf{f} \\ \mathbf{f}_*\end{pmatrix} \sim \mathcal{N}
\left(\boldsymbol{0},
\begin{pmatrix}\mathbf{K} & \mathbf{K}_* \\ \mathbf{K}_*^T & \mathbf{K}_{**}\end{pmatrix}
\right)\tag{2}\label{eq2}
$$

where $\mathbf{K}\_* = \kappa(\mathbf{X},\mathbf{X}\_\*)$ and $\mathbf{K}\_{\*\*} = \kappa(\mathbf{X}\_\*,\mathbf{X}\_\*)$. With $N$ training data and $N\_\*$ new input data  $\mathbf{K}$ is a $N \times N$ matrix , $\mathbf{K}\_\*$ a $N \times N\_\*$ matrix and $\mathbf{K}\_{\*\*}$ a $N\_\* \times N\_\*$ matrix. Using standard rules for conditioning Gaussians, the predictive distribution is given by

$$
\begin{align*}
p(\mathbf{f}_* \lvert \mathbf{X}_*,\mathbf{X},\mathbf{f}) &= \mathcal{N}(\mathbf{f}_* \lvert \boldsymbol{\mu}_*, \boldsymbol{\Sigma}_*)\tag{3}\label{eq3} \\
\boldsymbol{\mu_*} &= \mathbf{K}_*^T \mathbf{K}^{-1} \mathbf{f}\tag{4}\label{eq4} \\
\boldsymbol{\Sigma_*} &= \mathbf{K}_{**} - \mathbf{K}_*^T \mathbf{K}^{-1} \mathbf{K}_*\tag{5}\label{eq5}
\end{align*}
$$

If we have a training dataset with noisy function values $\mathbf{y} = \mathbf{f} + \boldsymbol\epsilon$ where noise $\boldsymbol\epsilon \sim \mathcal{N}(\mathbf{0}, \sigma_y^2 \mathbf{I})$ is independently added to each observation then the predictive distribution is given by

$$
\begin{align*}
p(\mathbf{f}_* \lvert \mathbf{X}_*,\mathbf{X},\mathbf{y}) &= \mathcal{N}(\mathbf{f}_* \lvert \boldsymbol{\mu}_*, \boldsymbol{\Sigma}_*)\tag{6}\label{eq6} \\
\boldsymbol{\mu_*} &= \mathbf{K}_*^T \mathbf{K}_y^{-1} \mathbf{y}\tag{7}\label{eq7} \\
\boldsymbol{\Sigma_*} &= \mathbf{K}_{**} - \mathbf{K}_*^T \mathbf{K}_y^{-1} \mathbf{K}_*\tag{8}\label{eq8}
\end{align*}
$$

where $\mathbf{K}\_y = \mathbf{K} + \sigma_y^2\mathbf{I}$. Although Equation $(6)$ covers noise in training data, it is still a distribution over noise-free predictions $\mathbf{f}\_\*$. To additionally include noise $\boldsymbol\epsilon$ into predictions $\mathbf{y}\_\*$ we have to add $\sigma_y^2$ to the diagonal of $\boldsymbol{\Sigma\_\*}$

$$
p(\mathbf{y}_* \lvert \mathbf{X}_*,\mathbf{X},\mathbf{y}) = \mathcal{N}(\mathbf{y}_* \lvert \boldsymbol{\mu}_*, \boldsymbol{\Sigma}_* + \sigma_y^2\mathbf{I})\tag{9}\label{eq9}
$$

using the definitions of $\boldsymbol{\mu}\_\*$ and $\boldsymbol{\Sigma}\_\*$ from Equations $(7)$ and $(8)$, respectively. This is the minimum we need to know for implementing Gaussian processes and applying them to regression problems. For further details, please consult the literature in the [References](#References) section. The next section shows how to implement GPs with plain NumPy from scratch, later sections demonstrate how to use GP implementations from [scikit-learn](http://scikit-learn.org/stable/) and [GPy](http://sheffieldml.github.io/GPy/).

## Implementation with NumPy

Here, we will use the squared exponential kernel, also known as Gaussian kernel or RBF kernel:

$$
\kappa(\mathbf{x}_i,\mathbf{x}_j) = \sigma_f^2 \exp\left(-\frac{1}{2l^2}
  (\mathbf{x}_i - \mathbf{x}_j)^T
  (\mathbf{x}_i - \mathbf{x}_j)\right)\tag{10}
$$

The length parameter $l$ controls the smoothness of the function and $\sigma_f$ the vertical variation. For simplicity, we use the same length parameter $l$ for all input dimensions (isotropic kernel).

```python
import numpy as np

def kernel(X1, X2, l=1.0, sigma_f=1.0):
    """
    Isotropic squared exponential kernel.

    Args:
        X1: Array of m points (m x d).
        X2: Array of n points (n x d).

    Returns:
        (m x n) matrix.
    """
    sqdist = np.sum(X1**2, 1).reshape(-1, 1) + np.sum(X2**2, 1) - 2 * np.dot(X1, X2.T)
    return sigma_f**2 * np.exp(-0.5 / l**2 * sqdist)
```

There are many other kernels that can be used for Gaussian processes. See \[3\] for a detailed reference or the scikit-learn documentation for [some examples](http://scikit-learn.org/stable/modules/gaussian_process.html#gp-kernels).

### Prior

Let's first define a prior over functions with mean zero and a covariance matrix computed with kernel parameters $l=1$ and $\sigma_f=1$. To draw random functions from that GP we draw random samples from the corresponding multivariate normal. The following example draws three random samples and plots it together with the zero mean and the *uncertainty region* (the 95% highest density interval computed from the diagonal of the covariance matrix).

```python
%matplotlib inline

from gaussian_processes_util import plot_gp

# Finite number of points
X = np.arange(-5, 5, 0.2).reshape(-1, 1)

# Mean and covariance of the prior
mu = np.zeros(X.shape)
cov = kernel(X, X)

# Draw three samples from the prior
samples = np.random.multivariate_normal(mu.ravel(), cov, 3)

# Plot GP mean, uncertainty region and samples
plot_gp(mu, cov, X, samples=samples)
```

![png](/img/2018-03-19/output_8_0.png)

The `plot_gp` function is defined [here](https://github.com/krasserm/bayesian-machine-learning/blob/dev/gaussian-processes/gaussian_processes_util.py).

### Prediction from noise-free training data

To compute the sufficient statistics i.e. mean and covariance of the posterior we implement Equations $(7)$ and $(8)$.

```python
from numpy.linalg import inv

def posterior(X_s, X_train, Y_train, l=1.0, sigma_f=1.0, sigma_y=1e-8):
    """
    Computes the suffifient statistics of the posterior distribution
    from m training data X_train and Y_train and n new inputs X_s.

    Args:
        X_s: New input locations (n x d).
        X_train: Training locations (m x d).
        Y_train: Training targets (m x 1).
        l: Kernel length parameter.
        sigma_f: Kernel vertical variation parameter.
        sigma_y: Noise parameter.

    Returns:
        Posterior mean vector (n x d) and covariance matrix (n x n).
    """
    K = kernel(X_train, X_train, l, sigma_f) + sigma_y**2 * np.eye(len(X_train))
    K_s = kernel(X_train, X_s, l, sigma_f)
    K_ss = kernel(X_s, X_s, l, sigma_f) + 1e-8 * np.eye(len(X_s))
    K_inv = inv(K)

    # Equation (7)
    mu_s = K_s.T.dot(K_inv).dot(Y_train)

    # Equation (8)
    cov_s = K_ss - K_s.T.dot(K_inv).dot(K_s)

    return mu_s, cov_s
```

and apply them to noise-free training data `X_train` and `Y_train`. The following example draws three samples from the posterior and plots them along with the mean, uncertainty region and training data. In a noise-free model, variance at the training points is zero and all random functions drawn from the posterior go through the trainig points.

```python
# Noise free training data
X_train = np.array([-4, -3, -2, -1, 1]).reshape(-1, 1)
Y_train = np.sin(X_train)

# Compute mean and covariance of the posterior distribution
mu_s, cov_s = posterior(X, X_train, Y_train)

samples = np.random.multivariate_normal(mu_s.ravel(), cov_s, 3)
plot_gp(mu_s, cov_s, X, X_train=X_train, Y_train=Y_train, samples=samples)
```

![png](/img/2018-03-19/output_12_0.png)

### Prediction from noisy training data

If some noise is included in the model, training points are only approximated and the variance at the training points is non-zero.

```python
noise = 0.4

# Noisy training data
X_train = np.arange(-3, 4, 1).reshape(-1, 1)
Y_train = np.sin(X_train) + noise * np.random.randn(*X_train.shape)

# Compute mean and covariance of the posterior distribution
mu_s, cov_s = posterior(X, X_train, Y_train, sigma_y=noise)

samples = np.random.multivariate_normal(mu_s.ravel(), cov_s, 3)
plot_gp(mu_s, cov_s, X, X_train=X_train, Y_train=Y_train, samples=samples)
```

![png](/img/2018-03-19/output_14_0.png)

### Effect of kernel parameters and noise parameter

The following example shows the effect of kernel parameters $l$ and $\sigma_f$ as well as the noise parameter $\sigma_y$. Higher $l$ values lead to smoother functions and therefore to coarser approximations of the training data. Lower $l$ values make functions more wiggly with wide uncertainty regions between training data points. $\sigma_f$ controls the vertical variation of functions drawn from the GP. This can be seen by the wide uncertainty regions outside the training data region in the right figure of the second row. $\sigma_y$ represents the amount of noise in the training data. Higher $\sigma_y$ values make more coarse approximations which avoids overfitting to noisy data.

```python
import matplotlib.pyplot as plt

params = [
    (0.3, 1.0, 0.2),
    (3.0, 1.0, 0.2),
    (1.0, 0.3, 0.2),
    (1.0, 3.0, 0.2),
    (1.0, 1.0, 0.05),
    (1.0, 1.0, 1.5),
]

plt.figure(figsize=(12, 5))

for i, (l, sigma_f, sigma_y) in enumerate(params):
    mu_s, cov_s = posterior(X, X_train, Y_train, l=l,
                            sigma_f=sigma_f,
                            sigma_y=sigma_y)
    plt.subplot(3, 2, i + 1)
    plt.subplots_adjust(top=2)
    plt.title(f'l = {l}, sigma_f = {sigma_f}, sigma_y = {sigma_y}')
    plot_gp(mu_s, cov_s, X, X_train=X_train, Y_train=Y_train)
```

![png](/img/2018-03-19/output_16_0.png)

Optimal values for these parameters can be estimated by maximizing the log marginal likelihood which is given by<sup>[1][3]</sup>

$$
\log p(\mathbf{y} \lvert \mathbf{X}) =
\log \mathcal{N}(\mathbf{y} \lvert \boldsymbol{0},\mathbf{K}_y) =
-\frac{1}{2} \mathbf{y}^T \mathbf{K}_y^{-1} \mathbf{y}
-\frac{1}{2} \log \begin{vmatrix}\mathbf{K}_y\end{vmatrix}
-\frac{N}{2} \log(2\pi) \tag{11}
$$

In the following we will minimize the negative log marginal likelihood w.r.t. parameters $l$ and $\sigma_f$, $\sigma_y$ is set to the known noise level of the data. If the noise level is unknown, $\sigma_y$ can be estimated as well along with the other parameters.

```python
from numpy.linalg import cholesky, det
from scipy.linalg import solve_triangular
from scipy.optimize import minimize

def nll_fn(X_train, Y_train, noise, naive=True):
    """
    Returns a function that computes the negative log marginal
    likelihood for training data X_train and Y_train and given
    noise level.

    Args:
        X_train: training locations (m x d).
        Y_train: training targets (m x 1).
        noise: known noise level of Y_train.
        naive: if True use a naive implementation of Eq. (11), if
               False use a numerically more stable implementation.

    Returns:
        Minimization objective.
    """

    Y_train = Y_train.ravel()

    def nll_naive(theta):
        # Naive implementation of Eq. (11). Works well for the examples
        # in this article but is numerically less stable compared to
        # the implementation in nll_stable below.
        K = kernel(X_train, X_train, l=theta[0], sigma_f=theta[1]) + \
            noise**2 * np.eye(len(X_train))
        return 0.5 * np.log(det(K)) + \
               0.5 * Y_train.dot(inv(K).dot(Y_train)) + \
               0.5 * len(X_train) * np.log(2*np.pi)

    def nll_stable(theta):
        # Numerically more stable implementation of Eq. (11) as described
        # in http://www.gaussianprocess.org/gpml/chapters/RW2.pdf, Section
        # 2.2, Algorithm 2.1.

        K = kernel(X_train, X_train, l=theta[0], sigma_f=theta[1]) + \
            noise**2 * np.eye(len(X_train))
        L = cholesky(K)

        S1 = solve_triangular(L, Y_train, lower=True)
        S2 = solve_triangular(L.T, S1, lower=False)

        return np.sum(np.log(np.diagonal(L))) + \
               0.5 * Y_train.dot(S2) + \
               0.5 * len(X_train) * np.log(2*np.pi)

    if naive:
        return nll_naive
    else:
        return nll_stable

# Minimize the negative log-likelihood w.r.t. parameters l and sigma_f.
# We should actually run the minimization several times with different
# initializations to avoid local minima but this is skipped here for
# simplicity.
res = minimize(nll_fn(X_train, Y_train, noise), [1, 1],
               bounds=((1e-5, None), (1e-5, None)),
               method='L-BFGS-B')

# Store the optimization results in global variables so that we can
# compare it later with the results from other implementations.
l_opt, sigma_f_opt = res.x

# Compute posterior mean and covariance with optimized kernel parameters and plot the results
mu_s, cov_s = posterior(X, X_train, Y_train, l=l_opt, sigma_f=sigma_f_opt, sigma_y=noise)
plot_gp(mu_s, cov_s, X, X_train=X_train, Y_train=Y_train)
```

![png](/img/2018-03-19/output_18_0.png)

With optimized kernel parameters, training data are reasonably covered by the 95% highest density interval and the mean of the posterior is a good approximation.

### Higher dimensions

The above implementation can also be used for higher input data dimensions. Here, a GP is used to fit noisy samples from a sine wave originating at $\boldsymbol{0}$ and expanding in the x-y plane. The following plots show the noisy samples and the posterior mean before and after kernel parameter optimization.

```python
from gaussian_processes_util import plot_gp_2D

noise_2D = 0.1

rx, ry = np.arange(-5, 5, 0.3), np.arange(-5, 5, 0.3)
gx, gy = np.meshgrid(rx, rx)

X_2D = np.c_[gx.ravel(), gy.ravel()]

X_2D_train = np.random.uniform(-4, 4, (100, 2))
Y_2D_train = np.sin(0.5 * np.linalg.norm(X_2D_train, axis=1)) + \
             noise_2D * np.random.randn(len(X_2D_train))

plt.figure(figsize=(14,7))

mu_s, _ = posterior(X_2D, X_2D_train, Y_2D_train, sigma_y=noise_2D)
plot_gp_2D(gx, gy, mu_s, X_2D_train, Y_2D_train,
           f'Before parameter optimization: l={1.00} sigma_f={1.00}', 1)

res = minimize(nll_fn(X_2D_train, Y_2D_train, noise_2D), [1, 1],
               bounds=((1e-5, None), (1e-5, None)),
               method='L-BFGS-B')

mu_s, _ = posterior(X_2D, X_2D_train, Y_2D_train, *res.x, sigma_y=noise_2D)
plot_gp_2D(gx, gy, mu_s, X_2D_train, Y_2D_train,
           f'After parameter optimization: l={res.x[0]:.2f} sigma_f={res.x[1]:.2f}', 2)
```

![png](/img/2018-03-19/output_20_0.png)

Note how the true sine wave is approximated much better after parameter optimization.

## Libraries that implement GPs

This section shows two examples of libraries that provide implementations of GPs. I'll provide only a minimal setup here, just enough for reproducing the above results. For further details please consult the documentation of these libraries.

### Scikit-learn

Scikit-learn provides a `GaussianProcessRegressor` for implementing [GP regression models](http://scikit-learn.org/stable/modules/gaussian_process.html#gaussian-process-regression-gpr). It can be configured with [pre-defined kernels and user-defined kernels](http://scikit-learn.org/stable/modules/gaussian_process.html#gp-kernels). Kernels can also be composed. The squared exponential kernel is the `RBF` kernel in scikit-learn. The `RBF` kernel only has a `length_scale` parameter which corresponds to the $l$ parameter above. To have a $\sigma_f$ parameter as well, we have to compose the `RBF` kernel with a `ConstantKernel`.

```python
from sklearn.gaussian_process import GaussianProcessRegressor
from sklearn.gaussian_process.kernels import ConstantKernel, RBF

rbf = ConstantKernel(1.0) * RBF(length_scale=1.0)
gpr = GaussianProcessRegressor(kernel=rbf, alpha=noise**2)

# Reuse training data from previous 1D example
gpr.fit(X_train, Y_train)

# Compute posterior mean and covariance
mu_s, cov_s = gpr.predict(X, return_cov=True)

# Obtain optimized kernel parameters
l = gpr.kernel_.k2.get_params()['length_scale']
sigma_f = np.sqrt(gpr.kernel_.k1.get_params()['constant_value'])

# Compare with previous results
assert(np.isclose(l_opt, l))
assert(np.isclose(sigma_f_opt, sigma_f))

# Plot the results
plot_gp(mu_s, cov_s, X, X_train=X_train, Y_train=Y_train)
```

![png](/img/2018-03-19/output_22_0.png)

### GPy

[GPy](http://sheffieldml.github.io/GPy/) is a Gaussian processes framework from the Sheffield machine learning group. It provides a `GPRegression` class for implementing GP regression models. By default, `GPRegression` also estimates the noise parameter $\sigma_y$ from data, so we have to `fix()` this parameter to be able to reproduce the above results.

```python
import GPy

rbf = GPy.kern.RBF(input_dim=1, variance=1.0, lengthscale=1.0)
gpr = GPy.models.GPRegression(X_train, Y_train, rbf)

# Fix the noise variance to known value
gpr.Gaussian_noise.variance = noise**2
gpr.Gaussian_noise.variance.fix()

# Run optimization
gpr.optimize();

# Obtain optimized kernel parameters
l = gpr.rbf.lengthscale.values[0]
sigma_f = np.sqrt(gpr.rbf.variance.values[0])

# Compare with previous results
assert(np.isclose(l_opt, l))
assert(np.isclose(sigma_f_opt, sigma_f))

# Plot the results with the built-in plot function
gpr.plot();
```

![png](/img/2018-03-19/output_25_0.png)

Although we can reproduce the kernel parameter optimization results, the variances of the predictions are still higher compared to previous results. This is because `GPy` includes noise variance $\sigma_y^2$ into predictions. This can be easily reproduced using Equation $(9)$

```python
mu_s, cov_s = posterior(X, X_train, Y_train, l=l_opt, sigma_f=sigma_f_opt, sigma_y=noise)

# Include noise into predictions using Equation (9).
cov_s = cov_s + noise**2 * np.eye(*cov_s.shape)

plot_gp(mu_s, cov_s, X, X_train=X_train, Y_train=Y_train)
```

![png](/img/2018-03-19/output_27_0.png)

Thanks for reading up to here :-) In another article, I'll show how Gaussian processes can be used for black-box optimization.

## References

\[1\] Kevin P. Murphy. [Machine Learning, A Probabilistic Perspective](https://mitpress.mit.edu/books/machine-learning-0), Chapters 4, 14 and 15.
\[2\] Christopher M. Bishop. [Pattern Recognition and Machine Learning](http://www.springer.com/de/book/9780387310732), Chapter 6.
\[3\] Carl Edward Rasmussen and Christopher K. I. Williams. [Gaussian Processes for Machine Learning](http://www.gaussianprocess.org/gpml/).

redpajama_set_name: RedPajamaGithub


text:
Wolf: I'll trade DRC for Kevin Kolb
By Arizona Sports | June 24, 2011 at 6:46 pm
UPDATED: June 24, 2011 at 7:56 pm
They say in life there are no guarantees. The same can be said when it comes to the Arizona Cardinals quarterback conundrum.
"There are no guarantees that you could trade for any veteran quarterback out there," Ron Wolfley said on Sports 620 KTAR's Doug and Wolf Friday morning. "There are no guarantees you could bring in a free agent. There are no guarantees that you could draft a quarterback No. 1."
If there is no guarantee it makes the rumor of trading cornerback Dominique Rodgers-Cromartie for Philadelphia Eagles Kevin Kolb an interesting proposition. Do you take a chance and send a former Pro Bowl defender for a quarterback who could possibly lead your franchise for the next decade?
"The question becomes about Dominique Rodgers-Cromartie," Wolf said. "It is speculation as to whether or not this deal is actually out there. If Rodgers-Cromartie would just change his approach there's no way I would do that. If DRC ever matures there's no way I'd do that deal. The question is will he ever mature? As it stands right now, I'm doing the deal. I'm going to pull the trigger on that. I'll trade DRC for Kevin Kolb."
Kolb may not be a sure thing, but the Cardinals need to take a chance when it comes to finding their next quarterback.
Whether it's Kolb, Kyle Orton or Carson Palmer, the Cardinals need to find a quality quarterback to lead the way. If they don't, the only thing that's guaranteed in 2011 is they'll struggle yet again.

redpajama_set_name: RedPajamaCommonCrawl


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What will this terminal command do?
Discussion in 'Mac Apps and Mac App Store' started by dogbone, Apr 8, 2006.
If I enter the above code exactly as is including the single quotes in Terminal and then drag my Application folder into terminal and execute, what will happen.
AFAIK, 'id -u' is not a flag that chown understands. My guess is that it will complain about syntax.
However, "id -u" will give the numerical UID of the current user.. I don't know if it would be called correctly from inside chown but it did.. this command would change the ownership of the application to the UID of whomever is the current user.
EDIT: I was right.. 'id -u' is an invalid argument.
Perhaps this person wanted you to do id -u in the Terminal FIRST, and then substitute that numerical UID for the 'id -u' portion.. which is how the syntax should go when using chown.
I've already been through the experience of trashing my system folder by a syntax error. Which is why I'm going to be absolutely sure this time before I do anything.
I'll have a look at that link it looks like it might do the trick. When I work out the correct code I'll confirm it first here to make sure I've got it right.
My gf has inherited my old computer and I've deleted all traces of me from the system but all the apps I installed have wacky permissions and ownership.
My goal is to change everything inside the Application folder to be owned by the proper owner of the computer and the group to be Admin, and all the permissions to be rwxrwxr--, then to run a repair permissions to change all the System apps back to their default values. I was given the above code but I'm not sure about it yet.
EDIT:, Just looked at the link and I'm not going to be able to work out the terminal commands on my own.
Repair permissions to fix any apps that require particular permissions.
Fantastic. worked like a charm. I really appreciate you answering this.


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text:
Tag: Betty Schott
Columns, War Bonds
Keeping my promise: A personal Pearl Harbor reflection
December 5, 2016 Cindy Hval
This week The Spokesman Review published a special keepsake section commemorating the 75th anniversary of the attack on Pearl Harbor. For the past nine years, I've been interviewing Pearl Harbor survivors for newspaper and was pleased to have many of those stories included.
In addition I wrote the following piece describing what it meant for me to visit the place I'd written about so often.
Never forget.
Cindy Hval, who wrote "War Bonds: Love Stories From the Greatest Generation," visited Pearl Harbor in March. She explored places she had learned about in nine years of interviewing Pearl Harbor survivors.
Stretching out, I pressed my cheek into the hot sand, its gritty heat almost too much to bear. Closing my eyes, I imagined the shriek of airplane engines and the spitting sound of machine gun fire hitting the beach, while the air around me burned.
I covered my head with my arms, and could almost hear the whistling sound of bullets whizzing past my ear.
A shadow loomed. "Are you okay?" my husband asked.
Slowly, I sat up and scooted back onto my brightly-colored beach towel.
"Just thinking about Nick," I said, while I slipped on my sunglasses.
The beauty of being married 30 years is I didn't have to explain what I meant.
Derek and I visited Oahu in March to celebrate our anniversary, but the trip was part pilgrimage for me. After nine years of interviewing Pearl Harbor survivors, I was at last visiting the place I'd written about so often.
Here on Waikiki, I was just 12 miles away from Hickham Field where Nick Gaynos almost lost his life on Dec. 7, 1941.
Nick Gaynos holding the piece of shrapnel that landed near him while under fire during the attack on Pearl Harbor 75 years ago. Gaynos died 20 days after this March 11, 2015, photograph. (Courtesy Cindy Hval)
During the attack on Pearl Harbor, Nick had been running toward his duty station when a Japanese pilot targeted him. He'd told me of looking up as he ran and seeing the grin on the pilot's face as he fired at him.
Nick hit the beach and covered his head with his arms as the bullets flew. When he got up he discovered a large piece of shrapnel next to him.
"I grabbed it," he said. "It was still hot from the explosion."
When my book "War Bonds: Love Stories From the Greatest Generation" was released, Nick attended a reading at the Coeur d'Alene Public Library in March 2015. He brought that piece of shrapnel with him. It was jagged and more than 2 feet long. He died a few weeks later.
Now, on the island that had been so devastated by the horrific attack, I carried his memories with me as well as those of Warren and Betty Schott. The Schotts had quarters on Ford Island and were eyewitnesses to the attack.
When Derek and I walked through the entrance of the Pearl Harbor Visitor Center, I wanted nothing more than to talk to Betty, to tell her I was here. But Betty passed away in July 2015.
At the center, we watched a short film featuring actual footage of the attack. A scene of sailors and soldiers pulling the wounded and dead from the harbor made me gasp. That's what Warren had done in the aftermath – it was the one thing he didn't want to discuss with me over the course of many interviews. It was the only thing he refused to speak of with his wife of 76 years. Now, watching the footage through tear-filled eyes, I finally understood why he was loath to speak of it.
That horror was also all too real for my friend Ray Daves. During the attack, he hustled to a rooftop and handed ammo to two sailors who were manning a .30-caliber machine gun. He had his own brush with death when a Japanese plane exploded 20 feet from that rooftop before crashing into the sea below. His left hand was lacerated by shrapnel.
Like Warren Schott, Ray spent time pulling wounded men from the harbor, his blood mingling with the red splashes in the water around him. In his biography, "Radioman," he described the bodies and body parts floating in the harbor. "We had to push them aside to get to the wounded," he said.
Despite those gruesome memories, what really choked him up was recalling the bombing of the USS Arizona.
"My friend George Maybee was on the Arizona," Ray said. "We'd gone through radio school together. Sat beside each other every day and were bunkmates at night."
Ray Daves
He watched as the Arizona burst into a huge fireball. He knew his friend was gone.
Over the years, Ray and I grew close. He reminded me so much of my dad. They were both from Arkansas and had joined the military seeking a way out of the poverty of the rural south. Both had tender hearts and shared a wickedly funny sense of humor.
The last time I spoke to Ray before his June 2011 death, I told him I longed to visit Pearl Harbor.
"George is there," he said, his eyes filling.
"I'll look for his name," I said. "I'll say a prayer."
Ray took my hand. "You do that, sweetheart."
Five years later, I boarded the boat that took us to the USS Arizona. As we stepped from the boat onto the memorial, the throng of tourists quieted. The only sound was the snapping of the flag in the wind and the clicking of cameras.
We were somber with the knowledge that we were standing on the final resting place of 1,102 of the 1,177 sailors and Marines killed on the Arizona.
A rainbow of undulating color in the water below caught my eye. Some 500,000 gallons of oil are still slowly seeping out of the ship's submerged wreckage, and it continues to spill up to nine quarts into the harbor each day.
Slowly, I entered the shrine. A marble wall bearing the names of those entombed beneath us stretched out behind a velvet rope.
So. Many. Names.
Overwhelmed, I looked at Derek. "I'll never find him," I whispered.
The day had been overcast, but suddenly a shaft of sunlight illuminated the marble.
"There," Derek said. "There he is – G.F. Maybee."
Bowing my head, I wept for the sailor I'd never met and for my friend who knew and loved him.
I hope that somehow Ray knows I kept my promise.
George Maybee hasn't been forgotten. Neither has Ray Daves.
Tagged authors, Betty Schott, books, Casemate Publishers, Cindy Hval, columns, Ford Island, George Maybee, Hickham Field, newspapers, Nick Gaynos, Oahu, Pearl Harbor, Pearl Harbor Survivors, Radioman, Ray Daves, The Spokesman-Review, USS Arizona, Veterans, Waikiki, War Bonds Love Stories From the Greatest Generation, Warren Schott, WWIILeave a comment
The house that love built
September 1, 2016 September 1, 2016 Cindy Hval
The other night I had a reading/signing event at Touchmark Retirement Community.
An employee approached me and said while she hadn't read War Bonds: Love Stories From the Greatest Generation, her daughter had.
It seems her daughter and her husband were looking for home and found one they really wanted in Millwood, WA.
"It wasn't the house so much, it was what they felt when they were inside it," the woman said. "There was such love in that house."
A neighbor chatted with them and told them the couple who had lived there had built the house and had been married for more than 70 years.
"Their story is in a book," he said.
Alas, the couple didn't get the house, but they did buy a copy of War Bonds. And they fell in love with Warren and Betty Schott, just like the rest of us.
Warren and Betty on their 75th anniversary
Tagged author events, authors, Betty Schott, book signings, books, Cindy Hval, Greatest Generation, homes, Love Stories, Millwood, Pearl Harbor Survivors, readers, The Greatest Generation, Touchmark Retirement Community, Veterans, War Bonds Love Stories From the Greatest Generation, Warren Schott, WWll2 Comments
Making Pearl Harbor Personal
March 29, 2016 Cindy Hval
I knew I was in trouble when I read the sign for Ford Island and starting crying.After many years of interviewing and writing about Pearl Harbor Survivors I was for the first time, walking where they walked.
My husband and I were celebrating our 30th anniversary on Oahu and Pearl Harbor was one of our first stops.
Chapter 11 of War Bonds: Love Stories From the Greatest Generation tells the story of Warren and Betty Schott who lived on Ford Island and both survived the horrific attack.
I pictured Warren's desperate drive to get his wife to safety. They'd spoken of shrapnel falling from the skies– of the road shredded by machine gun fire– of the terror and the noise.
We watched a short film featuring actual footage of the attack. A scene of sailors and soldiers pulling the wounded and dead from the Harbor made me gasp. That's what Warren had done in the aftermath– it was the one thing he didn't want to discuss with me over the course of many interviews. It was the only thing he refused to speak of with his wife and best friend of 76 years.
As we boarded the boat that took us to the USS Arizona, I thought of Pearl Harbor Survivor Ray Daves, who died in 2011. His friend George Maybee perished aboard the Arizona. His remains are entombed in the waters below the memorial. The throng of tourists quieted. The only sound was the snapping of the flag in the wind as I found Maybee's name among the more than 1,000 names engraved. I wished I could tell Ray.
All of the stories, all of the interviews over the years in no way prepared me for the magnitude, the solemness of this sacred place.
Remember Pearl Harbor. Indeed, I will never forget this place, these people, their sacrifice.
Here are links some of the stories I've written about those who survived the Day That Will Live in Infamy.
World War ll Vets Remember
World War ll Vets Educate Students
A Sailor Remembers
Fond Memories of Ray Daves Endure
Survivors of 1941 Attack Bring History to Life
Grateful for Vet's Story
Pearl Harbor Survivors Mark 73rd Anniversary in Spokane
The World has Lost Yet Another WWll Hero
Pearl Harbor Survivor's Story Comes to an End
Pearl Harbor Witness: 'It was so scary!'
Tagged anniversaries, Betty Schott, George Maybee, Hawaii, memories, Oahu, Pearl Harbor, Pearl Harbor Survivors, Ray Daves, Spokesman Review, travel, USS Arizona, Veterans, War Bonds Love Stories From the Greatest Generation, Warren Schott, writing, WWllLeave a comment
A funny thing happened on the way to the Google
October 7, 2015 July 17, 2018 Cindy Hval
I admit it. I Googled myself. Don't tell me you haven't! But what I found today, delighted me! Two reviews that I'd never seen.
The first was this lovely mention of War Bonds from a blog called Doodles and Words.
"War Bonds– Love Stories of the Greatest Generation by Cindy Hval is a collection of beautiful and loving memories of couples who met during World War II. She recounts how these men and women met and stayed together for decades despite many obstacles. Who doesn't love a good story? Well, what about 36 of them?
"Everything's built on friendship. He's been my best friend for 77 years." – Betty Schott"
And the second came from Pearl Harbor!
Pearl Harbor Survivor Couple – Betty and Warren Schott
"We first heard about the Pearl Harbor Survivor Couple, Betty and Warren Schott, in an article in the Spokesman-Review by Cindy Hval. This remarkable couple was living on Ford Island when Pearl Harbor was attacked.
They heard an explosion and Warren quickly recognized that Pearl Harbor was under attack from an enemy. Many others on Oahu at the time thought that it was a drill, but Warren saw the rising sun on the wing of a Japanese plane flying overhead.
Warren Schott watched as the USS Utah was torpedoed. He then took his wife and another family living below them to safety. Warren did not seek safety himself, instead he returned to Battleship Row to help victims of the attack.
"I took one of the boats and picked up our fellows who were in the water," he recalled. The men he pulled out were covered in oil.
Betty Schott did not sit idly by herself.
"They put us to work immediately, Betty said. "We unloaded guns and filled fire extinguishers."
This Pearl Harbor Survival Couple was married for 76 years before Warren Schott passed away in May 2014. Betty lived another year and passed away on July 5, 2015.
We appreciate the excellent story from Cindy Hval about this fascinating couple and the impression they left on her. You can read Ms. Hval's stories about the Schotts here and here or in her book below. We salute you Cindy Hval for your story and we salute the Schotts for their service to our country.
For more stories about love during wartime, read Hval's highly rated book: War Bonds."
Moral of the story? Don't be afraid to Google yourself– you might find nice surprises like these:-)
Tagged authors, Betty Schott, blogs, book reviews, books, Cindy Hval, Doodles and Words, Google, Pearl Harbor, Pearl Harbor Survivors, readers, Spokesman Review, War Bonds Love Stories From the Greates Generation, Warren Schott, writersLeave a comment
Saying goodbye to Betty
July 9, 2015 Cindy Hval
Today's Spokeman Review column.
Betty Schott (seated) wears a lei at a ceremony in 2014 to commemorate the 73rd anniversary of the attack on Pearl Harbor.
I loved to listen to her talk.
Though soft-spoken, Betty Schott, 98, had a sharp mind and an even sharper sense of humor. She smiled easily, laughed often, and called me "honey."
But when her husband of 76 years died in May 2014, her smile faded and the quips didn't come as quickly.
Adjusting to life without her beloved wearied her.
On Sunday, Betty died, 80 years and one day from the anniversary of her first date with Warren Schott.
I met the Schotts in 2007 when I interviewed them for my Love Story series. It was the start of a friendship that spanned eight years and immeasurably enriched my life.
From the beginning, a no-nonsense Warren assured me their story was no romantic tale. In fact, all those years ago, when a friend offered to set him up on a blind date with Betty, Warren scoffed, "Don't do me any favors."
He was a young sailor, not in the least interested in finding true love. But on July 4, 1935, love found him in the form of a beautiful, petite North Central High School graduate named Betty Forest.
They were married April 2, 1938, at the Wee Kirk O' the Heather chapel at Forest Lawn Cemetery in Los Angeles.
When I attended their 75th anniversary celebration, Betty quipped, "Well, we got married in a cemetery and honeymooned in Death Valley, so we got all that out of the way!"
But as Pearl Harbor survivors, the Schotts saw more than their share of death.
Warren had been sent to the Naval Air Station at Pearl Harbor shortly after their marriage. Betty was determined to join him and worked until she earned her passage. She arrived on Ford Island in 1939 and they settled into a tiny apartment near Battleship Row.
Their bedroom overlooked the island's runway, so they were accustomed to noise, but the sounds that woke them on Dec. 7, 1941, were unlike any they'd heard before.
Betty pulled on her robe and looked out the bathroom window. "Warren!" she called, "there's smoke and fire at the end of the runway."
Warren went to another window and spotted a plane flying low overhead. "I saw the red balls on the wings of the plane," he said. "I watched that plane torpedo the USS Utah. I said, 'Betty, we're at war!' "
While Betty filled fire extinguishers with other civilians in a supply warehouse, Warren had the grim job of pulling the dead and injured from the harbor. The men he pulled out of the water were covered in oil. Afterward, Betty discovered, "They got rid of every towel in my house trying to help clean them up. Finally they took down my kitchen curtains and used them."
Over the years, they talked about everything, but on one topic Warren remained silent. "He never talked about the people he pulled out of the oily water that morning," Betty said. "Never."
It was often painful for them to share their memories. "Slamming a door for days after the attack would make you jump," Betty said, recalling the terrible noise and confusion they experienced.
But the Schotts felt it was their duty to tell their story and to honor those who died that day.
Though they didn't think their 76-year marriage was anything remarkable, they were tickled that their story was included in "War Bonds: Love Stories From the Greatest Generation."
When I visited with Betty in December while working on a story about the 73rd anniversary of Pearl Harbor, I returned some photos she'd let me use for the book.
She reached up and patted my cheek with her soft, timeworn hand. "I'm so proud of you, honey," she said. And it felt like I'd received a blessing from my grandmother.
What I remember most was my last visit to her home – the home Warren had built, the home they'd shared for 65 years.
The plaque I'd seen years earlier still hung in the kitchen. It read, "Happiness is being married to your best friend."
Warren's death had left her adrift. She missed him so much, and she swore sometimes she could still see him sitting in his chair. She'd blink or turn her head and he'd be gone, but his presence was so real to her, his voice so compelling. Her own voice quavered when she said, "Every night at 11 p.m., he'd say, 'Honey, now it's time to go to bed.' "
That's why I would not be at all surprised if on Sunday morning, Betty heard him whisper, "Honey, now it's time to come on home."
And of course she went to him. How could she not? She said, "He's been my best friend for 77 years."
Contact Cindy Hval at dchval@juno.com. She is the author of "War Bonds: Love Stories From the Greatest Generation." Her previous columns are available online at spokesman.com/ columnists. Follow her on Twitter at @CindyHval.
Tagged authors, Betty Schott, books, Cindy Hval, death, Front Porch columns, loss, newspapers, Pearl Harbor Survivors, Spokesman Review, War Bonds Love Stories From the Greatest Generation, Warren Schott, WWll1 Comment
Saying goodbye is the hardest part
July 9, 2015 July 9, 2015 Cindy Hval
When you write a book about WWll veterans who are in their 80's and 90's you know your time with them is limited, but it doesn't make saying goodbye any easier.
Betty Schott died on July 5. She and her husband, Warren, survived Pearl Harbor together and their marriage spanned 76 years.
Warren and Betty Schott appearing in the Armed Forces Lilac Parade in Spokane, May 2010.
In this week's Spokesman Review column I say goodbye to Betty, one of the sweetest, wisest, kindest women I've ever known.
Her last words to me were, "I'm so proud of you, honey."
You can read the column here. Or here.
Tagged authors, Betty Schott, books, Cindy Hval, death, Front Porch column, loss, newspapers, Pearl Harbor Survivors, Spokesman Review, War Bonds Love Stories From the Greatest Generation, Warren Schott, WWll1 Comment
Pearl Harbor memories burn brightly for this couple
December 7, 2014 December 7, 2014 Cindy Hval
Warren and Betty Schott pictured here in Honolulu, in 1941, had an apartment just up from Battleship Row. Here's an excerpt from Chapter 11 of War Bonds, describing their eyewitness account of that terrible morning:
The couple was used to noise, but the sounds that woke them on Dec. 7, 1941, were unlike anything they'd heard before. Betty pulled on her robe and looked out the bathroom window.
"Warren!" she called, "there's smoke and fire at the end of the runway."
At first he didn't believe her. But at his wife's insistence, he went to another window and spotted a plane flying low overhead. "I saw the red balls on the wings of the plane," he said. "I watched that plane torpedo the USS Utah. I said, 'Betty, we're at war!'"
They hustled out of their quarters and stopped to pick up a young mother and her two kids who lived downstairs. "It was total chaos," said Warren of the surprise attack. "We didn't know what to do." The horrific noise of bombs, planes and machine gun fire added to the overwhelming terror.
Warren gathered everyone in the neighbor's car and took off for the administration building. "Barbara and I were in our nightgowns and robes, and shrapnel was falling from the sky," Betty said.
"The road was shredded by machine-gun fire," Warren said, as he recalled their frightening journey. Steering the vehicle away from the strafing fire of a Japanese warplane, he found shelter in a supply building. There Betty, her friend and the children, waited out the first wave of the attack. "They put us to work immediately, Betty said. "We unloaded guns and filled fire extinguishers."
Today, Betty dropped a lei at the new Pearl Harbor Survivors Memorial in Spokane, Washington. Warren passed away in March. They'd been married 76 years when he died.
Tagged Battleship Row, Betty Schott, Cindy Hval, Honolulu, Love Stories, Pearl Harbor, Pearl Harbor Survivors, Spokane, War Bonds, Warren Schott, Washington, WWllLeave a comment
Just had to write and let you know how much I enjoyed reading your latest column. I've been your fan forever, and now that my wife and I no longer spend winters in AZ, I won't miss any more of them.
― Larry Goehner.


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Q: Java: How to get the thumbnail from a file In windows explorer (and linux gnome) shows for each file a thumbnail or icon. Like with EXEs, images, videos, txt-files, ini-files, Word documents and so much other file types. Now is my question: Is there a way to get a (preferably large) icon by file.
Something like:
public static BufferedImage getThumbnail(File file) {...}

Thanks

A: I don't think the answers above are addressing the right question.  Martijn isn't asking for the API for manipulating icon images.  He wants to know how to get to the desktop's cache of thumbnail images for items in the browsable filesystem.
I don't think there's a portable way to do this at all, but the Linux world (Gnome and KDE) adhere to the Freedesktop thumbnail standard which can be read at: http://jens.triq.net/thumbnail-spec/
There may be code, perhaps in Gtk (but probably not Java) that implements a compatibility layer for windows, but I'm not aware of it if there is.

A: If you are looking for a plattform-independent (i.e. pure java) solution, hava a look at JavaThumbnailer. It's still beta, though, and has a limited number of supported file types.

A: It looks like there is no AWT way of doing this.
If you're using Swing, there is a method you can use to get a Swing Icon...
import javax.swing.filechooser.FileSystemView;
import javax.swing.Icon;

...
Icon ico = FileSystemView.getFileSystemView().getSystemIcon(file);

You can also convert that Icon back into an Image (most likely a BufferedImage, but I haven't tested it):
Image image = ((ImageIcon) ico).getImage();

There is also a class to get the icon directly, but this class is JDK dependent.  On Sun JDK's it's the sun.awt.shell.ShellFolder class.
If you're using SWT, things are a bit trickier.

A: Not entirely sure if you will be able to get the icon but take a look at AssociationService that is accessible using JDIC.
http://java.sun.com/developer/technicalArticles/J2SE/Desktop/jdic_assoc/
Also this thread http://forums.sun.com/thread.jspa?threadID=5357995

redpajama_set_name: RedPajamaStackExchange


text:
View across a sea ice floe during the Arctic summer, Spitsbergen island, Svalbard archipelago. Credit: Realimage/Alamy Stock Photo.
Limiting warming to 1.5C could 'substantially' cut risk of ice-free Arctic summers
Sea iceLimiting warming to 1.5C could 'substantially' cut risk of ice-free Arctic summers
Meeting the Paris Agreement's aspirational target of limiting global warming to 1.5C above pre-industrial levels could "substantially" reduce the risk of sea ice-free summers in the Arctic, research shows.
Two new studies find that, under 1.5C of warming, Arctic waters could experience ice-free summers around 2.5% of the time, or one in every 40 years. Under 2C, ice-free conditions could occur 19-34% of the time – or once every three to five years.
However, limiting warming to 1.5C will likely be not enough to prevent ice-free summers from occurring altogether, the researchers note.
Such dramatic loss of sea ice could drive further increases in warming and result in habitat loss for a wide range of species, including polar bears, seals and walruses, one of the authors tells Carbon Brief.
Out in the cold
The new studies, which are both published in Nature Climate Change, focus in on how efforts to curb climate change could affect summer sea ice cover in the Arctic.
After reaching its annual peak extent at the end of winter, Arctic sea ice contracts as temperatures rise through spring and summer. Sea ice then hits its yearly minimum sometime in September or early October.
Since the satellite record began in 1979, summer sea ice cover has fallen by around 13% per decade, with rising temperatures playing a large role in the decline.
With this trend expected to continue as global temperatures rise further, scientists have turned their attention to when Arctic summers could become "ice free". The term refers to a sea ice extent of less than one million square kilometres, rather than no ice cover at all.
The new research finds that limiting warming to 1.5C rather than 2C could "substantially" reduce the risk of ice-free conditions in the coming decades, says Prof Michael Sigmond, a research scientist at the Canadian Centre for Climate Modelling and Analysis at Environment Canada and lead author of one of the new studies. He tells Carbon Brief:
"We found that under 1.5C, only one in every 40 summers is expected to be ice free in the Arctic, whereas under 2C, one in every five summers is expected to be ice free."
A similar result was also obtained by Prof Alexandra Jahn, a climate modelling scientist from the University of Colorado Boulder and author of the second study. She tells Carbon Brief:
"I was surprised that half a degree of warming would make such a big difference. The probability of seeing any month-long ice-free conditions are strongly reduced if warming is limited to 1.5C."
Estimating ice loss
RCP8.5: The RCPs (Representative Concentration Pathways) are scenarios of future concentrations of greenhouse gases and other forcings. RCP8.5 is a scenario of "comparatively high greenhouse gas emissions" brought about by rapid population growth, high energy demand, fossil fuel dominance and an absence of climate change policies. This "business as usual" scenario is the highest of the four RCPs and sees atmospheric CO2 rise to around 935ppm by 2100, equivalent to 1,370ppm once other forcings are included (in CO2e). The likely range of global temperatures by 2100 for RCP8.5 is 4.0-6.1C above pre-industrial levels.
RCP8.5: The RCPs (Representative Concentration Pathways) are scenarios of future concentrations of greenhouse gases and other forcings. RCP8.5 is a scenario of "comparatively high greenhouse gas emissions" brought about by rapid population growth,… Read More
Both studies use modelling to assess the risk of an ice-free summer under a range of possible future scenarios.
Jahn's research uses the results from one climate model to to assess the impact of different emission scenarios on Arctic summer sea ice. The results are shown on the chart below, where the probability of an ice-free Arctic summer from 2020-2100 is estimated for each scenario.
These include a "business as usual" or high emissions scenario (RCP8.5; blue), an intermediate emissions scenario (RCP4.5; purple), a scenario where warming is limited to 2C (red), a scenario where warming is limited to 1.5C (black) and a scenario where warming is limited to 1.5C but with a temporary temperature overshoot (orange).
The probability of an ice-free Arctic summer from 2020-2100 under a range of future scenarios including 1.5C (black), 1.5C with temperature overshoot (orange), 2C (red), moderate emissions (RCP4.5; purple) and "business as usual" emissions (RCP8.5; blue). Source: Jahn. (2018)
The results suggest that, under a business-as-usual scenario, the Arctic is likely to experience an ice-free summer every year from around mid-century onwards, Jahn says.
Measuring melting
RCP4.5: The RCPs (Representative Concentration Pathways) are scenarios of future concentrations of greenhouse gases and other forcings. RCP4.5 is a "stabilisation scenario" where policies are put in place so atmospheric CO2 concentration levels off around the middle of the century, though temperatures do not stabilise before 2100. These policies include a shift to low-carbon energy technologies and the deployment of carbon capture and storage. In RCP4.5, atmospheric CO2 sits at 540ppm by 2100 – roughly 140ppm higher than now – equivalent to 630ppm once other forcings are included (in CO2e). By 2100, global temperatures are likely to rise by 2-3C above pre-industrial levels.
RCP4.5: The RCPs (Representative Concentration Pathways) are scenarios of future concentrations of greenhouse gases and other forcings. RCP4.5 is a "stabilisation scenario" where policies are put in place so atmospheric CO2 concentration levels… Read More
The second study uses a different climate model to simulate Arctic summer ice cover under a range of scenarios.
However, this research focuses on three scenarios where global temperatures become stable at 1.5C, 2C and 3C. Assessing stabilised temperatures – rather the point at which the limits are first reached – gives a clearer understanding of how mitigation could affect sea ice, Sigmond says:
"An important finding of our study is that the probability of ever reaching ice-free conditions continues to evolve after temperature stabilisation. Warming stabilization simulations are thus needed to properly assess the benefits of the Paris Agreement for Arctic sea ice."
The results are shown on the chart below, where ice-free probability is shown from present day until 2100 for each scenario, including 1.5C (blue), 2C (orange) and 3C (red). The ice-free probability is defined as the proportion of model simulations that reach ice-free conditions in each year.
The lines are cumulative, so they keep going up until all the simulations produce an ice-free summer, or until 2100 is reached. So, for example, under 2C or 3C, all models see an ice-free summer before 2040, whereas under 1.5C, only around 80% do by 2100.
The probability of an ice-free Arctic summer from present day to 2100 under warming of 1.5C (blue), 2C (orange) and 3C (red). Circles correspond to years when the warming threshold is first exceeded and squares correspond to years when the global mean temperature has stabilised. Source: Sigmond et al. (2018)
The results suggest that the projected frequency of ice-free conditions at 2C of warming is around eight times higher than 1.5C.
And, if the world were to warm by 3C, the Arctic could experience an ice-free summer more often than every other year by the end of the century.
Growing loss
Both studies find that, even if warming is limited to 1.5C, the risk of an ice-free Arctic is likely to grow larger over time.
This is because in addition to the long-term downward trend, there is also year-to-year natural variability in Arctic sea ice cover, explains Prof James Screen, a climate scientist from the University of Exeter who published a Nature News & Views article to accompany the new research.
He explains that, as time goes on, the chances of an episode of natural climate variability that leads to extremely low sea ice gets higher and higher. This, in turn, increases the probability of an ice-free Arctic, he writes:
"Consider the analogy of the probability of rolling a six with a standard six-sided die. For each roll of the die, the chance of rolling a six is 1-in-6 (17%) and the chance of not rolling a six is 5-in-6 (83%).
"The more rolls of the die, the greater the chance of rolling a six at least once…There is a 30% chance of rolling a six at least once in two throws and a 60% chance in five throws. By twenty-five throws, the odds of rolling a six at least once are 99%."
Ice-free summers could cause trouble for a range of wildlife, as well as people living and work in the Arctic region, Sigmond says:
"Loss of habitat directly impacts polar bears, seals and walruses, which use the ice for foraging, reproduction and resting, and for also for people who use ice for hunting, travel and other activities."
The disappearance of sea ice could also contribute to global warming by causing more heat to be absorbed by the ocean rather than reflected back into space by ice, he says:
"Ice loss also increases warming and can influence ocean circulation and weather – all of which can have impacts on people and ecosystems outside of the Arctic."
The two new studies add to the growing consensus that achieving the Paris target of 1.5C could "substantially" reduce the risk of ice-free summers, Screen says:
"There is therefore agreement across climate models that the probability of an ice-free Arctic in September would be substantially reduced by achieving the 1.5C target of the Paris Agreement."
Both studies make an "important contribution" to our understanding of how climate change is likely to affect Arctic sea ice, says Dr Amber Leeson, a lecturer in glaciology and environmental data science from the University of Lancaster, who was not involved in the research. She tells Carbon Brief:
"Each study uses a different climate model to come up with broadly the same conclusions – that if warming at 2C above pre-industrial temperatures is reached, and sustained, then we are locked in to an ice-free Arctic at least once before the end of the century."
However, each study bases its results on a single climate model and so cannot account for potential differences between models, she says:
"Given the importance of these findings for climate change policy however, repeating this work in the context of a multi-model analysis – for example CMIP6 – is now a pressing concern."
Jahn, A. (2018) Reduce probability of ice-free summers for 1.5C compared to 2C warming, Nature Climate Change, http://nature.com/articles/doi:10.1038/s41558-018-0127-8
Sigmond, M. et al. (2018) Ice-free Arctic projections under the Paris Agreement, Nature Climate Change, http://nature.com/articles/doi:10.1038/s41558-018-0124-y
Ice-free Arctic summers to occur 'every three years' with 2C of global warming