Answers.Body: <p><strong>Does it classify as Machine Learning?</strong>
  If I understand the problem correctly, my opinion is <em>yes, this is machine learning</em>.  In fact, I think it is just linear regression for finding the equation of a <em>horizontal line</em> <code>y(t) = a</code> that fits the the dataset <code>y(t) = Xt</code>.</p>
  
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Answers.CreationDate: 2022-10-24T02:13:45.203Z
Answers.LastActivityDate: 2022-10-24T02:13:45.203Z
Answers.UserDisplayName: Snehal Patel
Body: <p>I have a gaussian distributed time series (<span class="math-container">$X_t$</span>) with some parameters in my experiment. Suppose I want to know the mean <span class="math-container">$\mu$</span>. If I define another time series <span class="math-container">$Y_t$</span> such that <span class="math-container">$Y_t=X_t-a$</span> for all <span class="math-container">$t$</span>. Now say I vary this parameter <span class="math-container">$a$</span> and generate altogether different time series for each <span class="math-container">$a$</span>, say <span class="math-container">$Y_t(a)$</span>. I look at the mean of <span class="math-container">$Y_t$</span> for each <span class="math-container">$a$</span>. The value of a, where I get the mean of <span class="math-container">$Y_t$</span> closest to <span class="math-container">$0$</span>, will be my estimate of <span class="math-container">$\mu$</span>. Say I will eventually use this learnt value of <span class="math-container">$\mu$</span> to generate <span class="math-container">$Y_t$</span> as my final goal. Can this be called ML? I am using some training data of <span class="math-container">$X_t$</span> to learn about its parameter and then using test data of <span class="math-container">$X_t$</span> to generate <span class="math-container">$Y_t$</span>.</p>
  <p>Now why am I working so hard on this simple problem? Well, actually I am not. I am doing something else, which will have lots of parameters in the time series and will be used to generate other time series after similar parameter extraction. That will be too complicated to discuss here. I just wanted to clear my basics using an over-simplified example.</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2020-04-25T23:44:40.893Z
Comments.Text: I don't understand what you mean by "gaussian distributed time series". Can you precisely define it? Are you saying that each element of the time series is sampled from 1. the same or 2. possibly different Gaussian? In general, I don't fully understand your problem. Do you have the original time series $X_t$? If not, do you want to estimate it from "noisy" similar time series? I don't understand how subtracting $a$ from $X_t$ gives you any insight. Also, I don't understand how you are going to generate $Y_t$ if you don't have $X_t$. Are you assuming that $Y_t$ is $X_t -a$, for some $a$?
Comments.UserDisplayName: nbro
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2020-04-27T17:40:18.313Z
Comments.Text: @nbro Thanks for your response. The time series $X_t$ is given, and we know it has a Gaussian distribution, (histogram: Gaussian). So each point in $X_t$ belongs to a gaussian distribution with the same mean and variance. Now if you subtract a from each point in $X_t$ to construct a different series $Y_t$ the mean of the gaussian shifts. For some $a$, the constructed $Y_t$ has 0 mean. What I am asking if you vary $a$ and try to see for what $a$ this is achieved, then use that correctly found a, to generate more data points of $Y_t$, from $X_t$ can I call it as ML?
Comments.UserDisplayName: Raunak Dey
Tags: <machine-learning><classification><terminology><time-series>
Title: Does it classify as Machine Learning?
UserDisplayName: Raunak Dey
ThreadText: # Does it classify as Machine Learning?
  
  (Asked by: username_0 on 2020-04-25)
  
  I have a gaussian distributed time series ($X\_t$) with some parameters in my experiment. Suppose I want to know the mean $\mu$. If I define another time series $Y\_t$ such that $Y\_t=X\_t-a$ for all $t$. Now say I vary this parameter $a$ and generate altogether different time series for each $a$, say $Y\_t(a)$. I look at the mean of $Y\_t$ for each $a$. The value of a, where I get the mean of $Y\_t$ closest to $0$, will be my estimate of $\mu$. Say I will eventually use this learnt value of $\mu$ to generate $Y\_t$ as my final goal. Can this be called ML? I am using some training data of $X\_t$ to learn about its parameter and then using test data of $X\_t$ to generate $Y\_t$.
  
  Now why am I working so hard on this simple problem? Well, actually I am not. I am doing something else, which will have lots of parameters in the time series and will be used to generate other time series after similar parameter extraction. That will be too complicated to discuss here. I just wanted to clear my basics using an over-simplified example.
  
  **Tags:** machine-learning, classification, terminology, time-series
  > **Comments:**
  > **username_1**: I don't understand what you mean by "gaussian distributed time series". Can you precisely define it? Are you saying that each element of the time series is sampled from 1. the same or 2. possibly different Gaussian? In general, I don't fully understand your problem. Do you have the original time series $X_t$? If not, do you want to estimate it from "noisy" similar time series? I don't understand how subtracting $a$ from $X_t$ gives you any insight. Also, I don't understand how you are going to generate $Y_t$ if you don't have $X_t$. Are you assuming that $Y_t$ is $X_t -a$, for some $a$?  
  > **username_0**: @nbro Thanks for your response. The time series $X_t$ is given, and we know it has a Gaussian distribution, (histogram: Gaussian). So each point in $X_t$ belongs to a gaussian distribution with the same mean and variance. Now if you subtract a from each point in $X_t$ to construct a different series $Y_t$ the mean of the gaussian shifts. For some $a$, the constructed $Y_t$ has 0 mean. What I am asking if you vary $a$ and try to see for what $a$ this is achieved, then use that correctly found a, to generate more data points of $Y_t$, from $X_t$ can I call it as ML?  
  
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  ## 1 answers
  
  ### Answer by username_2 on 2022-10-24. Score: 0
  
  **Does it classify as Machine Learning?**
  If I understand the problem correctly, my opinion is *yes, this is machine learning*. In fact, I think it is just linear regression for finding the equation of a *horizontal line* `y(t) = a` that fits the the dataset `y(t) = Xt`.
  
  
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