text:
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redpajama_set_name: RedPajamaCommonCrawl


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text:
\section{Introduction}

Online marketplaces that rely on user-generated ratings to judge the quality of listings on their platform, such as Amazon or Uber, suffer from a \textit{cold-start} problem, where a new listing is unable to be rated accurately because it has little to no review data. This impacts the ability for new listings with a single bad rating to gain notoriety, and also allows for bad listings that happen to receive a few good reviews to be unfairly promoted. Cold-start's consequences are well-documented in the context of recommender systems, where it is referred to as the \textit{new user problem} \cite{marlin2004collaborative}, and it is particularly problematic for online labour markets, where workers with little experience are unlikely to be hired \cite{pallais2014inefficient}.

Most online marketplaces calculate the estimated quality score of a product on the market using previous ratings that product has received, most commonly in the form of a sample mean. This leads to a problem in the context of cold-start; the first few ratings for a product could simply be the result of luck or malicious behaviour. For example, a high-quality product may have just gotten unlucky with a few bad ratings, or a poor-quality product may have found a way to "buy" a batch of fradulent reviews (perhaps by leaving high-quality ratings through sock-puppet accounts). As such, the naively estimated quality of the product from early ratings alone might not correspond to the actual ratings a product gets in the future. A better solution would be to be more lenient to new products with few ratings, or, better yet, consider information about how other similar products performed when they had only a few ratings.

We suggest a \textit{parametric empirical Bayes} (EB) algorithm to estimate the quality of a product, which takes into account more than just the past reviews of a product to generate a quality estimate. EB is a Bayesian estimation process; it assumes that there exists some prior distribution of quality from which products are drawn, and uses the individual ratings of the product to compute a posterior. Rather than use an uninformative prior or assume some outside knowledge about the parameters of the prior, EB fits this prior through empirical observations about the distribution of ratings in the overall population. This simple-to-use method exploits the fact that most online marketplaces have large amounts of \textit{parallel} data at the product level: there are many items on the market, each of which have their own ratings data. When a new product enters the market, we should be able to leverage our knowledge about similar products that already exist to temper our expectations of the quality of the new good. Using the average quality of each product in a population, we can fit a prior over what the quality of a new good in an existing population will be. We then treat any user reviews for that new good as updates to the prior distribution, using this information to present a quality estimate.

We test this approach on a dataset of Amazon reviews, comparing the quality of estimation to naively computing the sample mean (what we call the \textit{frequentist approach}), with a particular interest in how either method works in low data regimes. To control for potential selection issues in the data generation process, we also replicate this analysis on synthetic data. We find that for all datasets, the empirical Bayes approach has lower overall mean-squared error, with dramatic improvements on products with few ratings: On the Amazon dataset, we achieve an average 72\% reduction in mean-squared error when the EB algorithm sees a product with 10 or fewer reviews. However, EB also gives less accurate predictions on "outlier" products that have unusually high or low quality scores relative to the population, until enough ratings are received for the outlier to overcome EB's initial skepticism. We finish with a discussion of why we believe an implementation of our model in a real-world market would require modelling the ratings generation process as endogenous to the model, rather than simply being given as training data.

\section{Related Work}

Empirical Bayes methods have been well-studied and widely used in statistics literature since their introduction by Robbins~\cite{robbins1992empirical}, most notably for the method's applications in statistical decision theory~\cite{robbins1964empirical}. Empirical Bayes also has a long history of being used for statistical inference \cite{morris1983parametric,efron2001empirical,bastani2021efficient}; to our knowledge, our work is the first to use EB for statistical inference rating systems for online marketplaces. Ignatiadis and Wager~\cite{ignatiadis2019covariate} infer the quality of movies with empirical Bayes estimators when one has access to feature-level data for each movie in addition to ratings, but mainly emphasize the general minimax optimality bounds for their approach.

On the ratings system side of literature, user-generated reviews as a feedback system have become increasingly widespread in online platforms over the past two decades \cite{dellarocas2003digitization}. Empirical experiments have shown the importance of early ratings on a product's success on online marketplaces~\cite{cabral2010dynamics}, as well as the possible impacts that social influence can have on an item's success~\cite{salganik2006experimental,bolton2013engineering}. To investigate these effects, many empirical studies have implemented novel ratings system and analyzed their impacts: \citet{gaikwad2016boomerang} design an online labour marketplace where the raters' judgements have consequences for future transactions, while \citet{garg2021designing} assess how changing the language of the surveys presented to raters can drastically alter ratings scores. From a more theoretical, model-building perspective, \citet{garg2019designing} designed an optimal ratings system to recover the true quality of products in a \textit{binary} rating system where the rating can either be 0 (dislike) or 1 (like). Most related to our work, \citet{kokkodis2015reputation} use Bayesian methods and linear dynamical systems to predict the quality scores of individuals in online labour markets when those individuals participate in multiple different categories of work.

\section{Model and Method}

In this section, we develop a model to formalize our ratings problem. The key assumption of this model is that every product in an online market has a true quality score that is drawn from an underlying \textit{population distribution} of items, and that, with enough ratings data for an individual product, the estimated quality of that product resembles the true quality. Our goal will be to estimate the true quality of a product, even if there are not many ratings for it. We take a Bayesian approach: We will treat the population distribution as our prior, and the ratings-generation process for a single product as our data-generating process.

We assume we are given a dataset of products $R$, with each product having some number of 1-, 2-, 3-, 4-, and 5-star ratings. While EB is a statistical method that works for many distributions, for simplicity, we model each product $r \in R$ as generating ratings according to a multinomial distribution with event probability parameters $p_{1r}...p_{5r}$. Each product $r$ has $N_r$ reviews, with $r_i \leq N_r$ referring to the number of $i$-star reviews garnered by a product.

For each product, we model $(p_{1r},...p_{5r})$ as being drawn from a Dirichlet distribution with parameters $\alpha = (\alpha_1...\alpha_5)$, which represents a population that the products are being drawn from. Unlike a traditional Bayesian approach, in which the parameters of the prior are either set to be uninformative or given as hyperparameters, in parametric empirical Bayes, we fit $\alpha$ using population-level data. For each product $r$, we estimate the event probability parameter for an $i$-star review to be $\hat{p_{ir}} = r_i/N_r$. This reflects our assumption that, provided each product in the training dataset has enough reviews, the estimated event probability parameter resembles the true event probability parameter.

We use these estimates to calculate a maximum-likelihood estimate of $\alpha$. To compute MLEs $\hat{\alpha_1}...\hat{\alpha_5}$ from the set of probability parameter estimates $\{(\hat{p}_{1r}...\hat{p}_{5r})\}_{r \in R}$, we use an iterative method for calculating the maximum likelihood estimators of the Dirichlet distribution parameter~\cite{huang2005maximum}: If $\hat{\alpha_{t,i}}$ is the estimate for $\alpha_i$ at iteration $t$, the update rule is

\begin{align}
    \hat{\alpha}_{t+1,i} &= \psi^{-1}\left(\psi\left(\sum_{j=1}^5 \hat{\alpha_{t,j}}\right) + \frac{1}{N}\sum_{r \in R} \log(\hat{p_{ir}})\right),
\end{align}

where $\psi$ is the digamma function. We iterate until convergence is achieved, getting the prior parameter estimate $\hat{\alpha} = (\hat{\alpha}_1...\hat{\alpha}_5)$. To estimate the quality of a new product $d$ with observed number of $i$-star reviews $d_i$ for $i \in \{1...5\}$, we exploit conjugacy and find

\begin{align} \label{postupdate}
    \textrm{prob}(p_{1d}...p_{5d}|d_1,d_2...d_5) \sim \textrm{Dirichlet}(\hat{\alpha_1}+d_1...\hat{\alpha_5}+d_5)
\end{align}

We compute the posterior mean estimates $(\tilde{p_{1d}}...\tilde{p_{5d}})$ from this distribution as our empirical Bayes estimates of the event probability parameter of getting an $i$-star review for product $d$.

Throughout the next section, we contrast quality estimates derived from these posterior means with the \textit{frequentist approach} for estimating product quality, which we define here to simply be the sample mean of a product's existing ratings: If we have a new product $d$ with observed number of $i$-star reviews $d_i$ for $i \in \{1...5\}$, the frequentist approach estimate of $p_{id}$ is simply $d_i/\sum_jd_j$. This is equivalent to the maximum likelihood estimator in a frequentist setting, and is what many large online platforms, like Uber, use for calculating estimated quality scores~\cite{uber}.

\section{Experiments}

The primary goal of our experiments is to investigate how our empirical Bayes estimation method compares to traditional frequentist estimation. We are particularly interested in the performance of these estimators in low-data regimes, as well as identifying if there are any trade-offs between the two methods, and looking at specific examples of products that gain or lose significantly when moving from frequentist quality estimates to EB. We chose to use R to implement our experiments; all of the code and data for our experiments can be found at [\url{https://github.com/LEFTA98/empirical_bayes}], including code for generating the synthetic datasets.

For each of the datasets below, we split the users 60-40 into a train-test split. After training a prior using the training subset with the method described in Section 3, we carry out our analysis as follows: First, we filter out any products with fewer than 100 reviews, then cap any remaining products at exactly their 100 earliest reviews. We further split this set into a \textit{learning set} and \textit{evaluation set}, where the former contains the first 50 reviews for each test set product and the latter contains the last 50 reviews for each test set products. Let $r^{\textrm{learn}}_i$ ($r^{\textrm{eval}}_i$) refer to the number of $i$-star reviews for product $r$ in the learning set (evaluation set), and $N_r^{\textrm{learn}}$ ($N_r^{\textrm{eval}}$) be the total number of reviews for product $r$ in the learning set (evaluation set). While filtering out data with fewer than 100 data points seems counterintuitive to solving the cold start problem, we take this approach so that we have a reliable ground-truth estimate of what the quality of a product is through the evaluation dataset; we investigate cold-start in this context by limiting the number of ratings per user in the learning set the algorithm sees.

\subsection{Datasets}

We make use of a dataset of reviews for 71,982 products listed under the "Video Games" section on Amazon, sold on the platform from 1997 to 2018. We chose to use this dataset because of the quantity of data available, and because of its relative reliability: While the distribution of ratings among products in this dataset is heavily left-tailed (see Figure 1), it is actually more heterogeneous than most product categories on Amazon, with all average ratings from 1 to 5 being adequately represented. There were about 2,565,349 distinct reviews in this dataset, which is public and available online~\cite{jianmo}.

To investigate how our model works on differently distributed data, we also create synthetic datasets. We generate two synthetic datasets---the first assumes the true Dirichlet parameters to be $\alpha = (1,1,1,1,1)$, which induces a uniform prior, creating a population where the average quality is centered around 3 stars. It then draws a value $(p_1...p_5)$ from this prior to create a synthetic product, then draws from a Multinomial$(100, (p_1...p_5))$ distribution to generate 100 ratings for this product. We repeat this 10,000 times for a total of 1 million data points, and call this the \textit{uniform} dataset. The next dataset investigates what may happen if the data-generation process is endogeneous to the true quality of each product; low-quality products may be more likely to self-censor by exiting the market early or be deprioritized by the platform's search and ranking algorithms, and hence be less likely to generate reviews. We create a \textit{scaled} dataset which draws user parameters $(p_1...p_5)$ from a uniform prior as before, except now, the number of the trials in the multinomial ratings generation process is decided by a Poisson($\lambda$) random variable, where $\lambda$ is a rate hyperparameter that should be a function of the true quality of the product. For the purposes of this experiment we choose $\lambda = \frac{100}{3}\sum_{i=1}^5 ip_{i}$. This ensures that most products who are above-average quality will be above the 100-number cutoff for the test set, though there will be significantly less representation of lower-than-average products in our experiments; in practice, this should not change the distribution of ratings across products, but will significantly impact the availability of data for low-quality goods.

After splitting each dataset into train and test sets, we use the training data to fit a Dirichlet prior for each dataset, as per Section 3, filtering out from the training set any products with fewer than 20 reviews. Histograms of the average rating of each good in each dataset are shown in Figure 1 for products that have 20 or more reviews (and hence would not be filtered out from the experiment).

\begin{figure}
  \begin{center}
    \includegraphics[scale=0.25]{figures/f1.png}
  \end{center}
  \caption{Histograms showing distribution of average ratings of products with 20 or more reviews for different datasets. Note the heavy left-tailed skew for the Amazon dataset. Ratings for products in the scaled synthetic dataset were generated at a rate proportional to the true quality of the product. Note that this did not change the distribution of ratings of products in the scaled dataset compared to the uniformly generated synthetic dataset, though it does affect availability of ratings data for low-quality goods. }
\end{figure}

\subsection{Over-time comparison of EB and frequentist}

The main advantage that we find the EB model to have over the frequentist approach is in how accurately it predicts the true quality of a product based on very few datapoints. We find that, when looking at the population-level mean-squared error, EB performs significantly better than the frequentist approach, with the largest gains being made in low-data regimes where there are few training examples for each product.

Our first experiment looks at how accurately the empirical Bayes posterior mean can estimate the true quality of a product when compared against the frequentist approach. We assume that for each product $r$ in the test set of products, the proportion of $i$-star ratings it gets in the evaluation set is equivalent to the true probability parameter; that is, we assume $p_{ir} = r^{\textrm{eval}}_i/N^{\textrm{eval}}_i$. For example, if 10 out of the 50 product reviews for product $r$ in the evaluation set are 4-star reviews, we assume that the true probability that a review is 4 stars for $r$ is $1/5$. Given a set of estimators $\{\hat{\theta}_{ir}\}_{i \in \{1...5\}, r \in R}$, we define the \textit{mean-squared error} to be $\frac{1}{|R|} \sum_{r \in R}\sum_{i=1}^5 (\hat{\theta}_{ir} - p_{ir})^2$. Also of note for our later experiments will be the \textit{per-product mean-squared error}, which is computed for a given product $r$ and given by $\sum_{i=1}^5 (\hat{\theta}_{ir} - p_{ir})^2$, and the \textit{estimated quality} of a given product $r$, calculated as $\sum_{i=1}^5 i\hat{\theta}_{ir}$.

We compare the posterior mean calculated from equation \eqref{postupdate} with the frequentist approach, which computes $r^{\textrm{learn}}_i/N^{\textrm{learn}}_i$ as the estimate for the $i$th event probability parameter for product $r$ and does not use data from the training set. Figure 2 shows our observations of this comparison, where we vary the number of reviews that each product in the learning set gives to the model, ordered from oldest reviews first to newest reviews last. In all datasets, we see that our EB estimator achieves a lower mean-squared error than the frequentist approach at all learning window sizes, with the greatest improvements made when the number of training examples seen is low. In particular, the mean-squared error for EB dips below 0.1 for all datasets after seeing just 3 learning examples, compared to 12 learning examples for the frequentist approach on the Amazon dataset. Note the MSE for both estimates approach each other as the number of reviews increases; this fits the natural Bayesian intuition of the prior being overwhelmed by data as the number of learning examples increases.

\begin{figure}
  \begin{center}
    \includegraphics[scale=0.22]{figures/f2.png}
  \end{center}
  \caption{Comparison of mean-squared error of empirical Bayes versus frequentist quality estimation, indexed by number of learning examples seen. The y-axis represents the mean-squared error. In all datasets, EB's gains over the frequentist approach are greatest in low-data regimes where the cold-start problem traditionally exists; after that, both methods converge to the same estimates. }
\end{figure}

Figure 2 shows the advantages of EB in cold-start scenarios: Empirical Bayes performs better than frequentist in low-data regimes. However, Empirical Bayes does not perform well across all products. This is seen in Figure 3, which plots the per-product mean squared error, stratified across the "true quality" of the product $\sum_{i=1}^5 ir^{\textrm{eval}}_i/N_r$. We observe that, in settings with few learning examples, EB gives good quality estimates for products with true ratings that were commonly present in the training data of the EB prior---in the case of the Amazon dataset, this value is roughly around 4 stars. However, products with true quality ratings that were not common in the population, such as 1-star products in the Amazon dataset, did better under the frequentist procedure when there were few learning examples. This suggests that the empirical Bayes estimator performs better on common products and does worse on outliers, while the frequentist estimator performs similarly on all products. Also of note are the results for the scaled dataset: Due to the lower number of ratings for low-quality goods, we have no information on products with a rounded quality score of less than 2, as many low-quality goods had an insufficient quantity of reviews to meet the test set cutoff of 100 reviews or more. This could imply an underrepresentation of low-quality goods in the Amazon dataset: if the true underlying data generation process for the Amazon dataset was dependent on the true quality of each product, as it was in the scaled dataset, then truly low-quality Amazon products would have less ratings and might not be included in fitting the EB algorithm.

\begin{figure*}
  \begin{center}
    \includegraphics[scale=0.3]{figures/f3wide.png}
  \end{center}
  \caption{Comparison of empirical Bayes versus frequentist quality estimation, stratified by true quality of the product, rounded to the nearest multiple of 0.5. The EB estimation error is lowest around the most common true quality scores for that dataset, but the frequentist approach beats EB on products with uncommon true quality scores relative to the population. The columns show the number of learning examples used.}
\end{figure*}

\begin{figure*}
    \begin{center}
    \includegraphics[scale=0.26]{figures/ebgoodfig.png}
    \includegraphics[scale=0.26]{figures/ebbadfig.png}
    \caption{Figures 4(a) (left) and 4(b) (right): Estimated quality of individual Amazon products indexed by number of learning examples. 4(a): the estimated quality of the product for which the one-datapoint frequentist estimator was furthest from the true average. 4(b): the estimated quality of the product for which the difference between the 50-datapoint EB estimator and ground truth was furthest off from the difference between the 50-datapoint frequentist estimator and ground truth. The straight line represents the true average, while the black dots represent individual ratings. EB does well for products that get bad ratings but improve over time, but for products with an uncommon true average, EB is eclipsed by frequentist estimation.}
    \end{center}
    \label{fig:my_label}
\end{figure*}

\subsection{Investigating individual products most impacted by empirical Bayes}

In this subsection, we analyze individual products in the Amazon dataset with estimated qualities that differ the most when swapping out the frequentist approach for the EB estimator. Figure 4(a) shows the estimated quality, indexed by number of learning examples seen, for the product with the largest possible difference between its true average score and the frequentist approach's estimated quality when using only one learning example. This particular product benefited greatly from EB, as it received many poor ratings early on, but gradually improved: When there were few data points, EB was willing to put more weight into the prediction that the product was close to the average population quality, which ended up being indicative of the good's true quality.

Conversely, Figure 4(b) shows a similar graph to 4(a), but for product that benefited the most after 50 learning examples from using the frequentist approach instead of EB. We quantify this by taking the good for which (difference between ground-truth, EB estimate) - (difference between ground-truth, frequentist estimate) was largest. This product received mostly 1-star reviews, though it had a few good reviews at the beginning. Despite the overwhelmingly negative feedback from ratings, there were still enough 5-star ratings for this product so that the prior from empirical Bayes was still not overwhelmed after 50 learning examples. Note that our analysis from Section 4.2 suggests that there are far more items within the population that resemble the product in Figure 4(a), rather than the product in Figure 4(b). If this were not the case, then the fitted population prior would have instead had more probability mass towards lower-quality goods, meaning EB would have been more likely to believe goods were low-quality when operating off few datapoints, and so the EB estimate for Figure 4(b) would be lower. Figure 4 highlights a key limitation of our relatively simplistic EB model: Depending on which is more common in the underlying population, EB can either correct for products that ranked unusually low for their first few reviews, or for products that ranked unusually high for their first few reviews, but not for both at the same time.

\section{Future work}

Many open directions remain from this study. EB could be used as an approach to model \textit{transfer learning} in online marketplaces, where one tries to estimate the quality of a worker or product in a new market based on their past performance in previous market(s), such as in \cite{kokkodis2015reputation}. We believe, however, that the potential endogeneity of data generation mentioned in Section 4 is one of the most important aspects of this problem to work on. Because online platforms usually give highly-rated goods more exposure, it would be reasonable to assume that ratings are generated adaptively in response to the currently estimated quality of a product. If the product has a high estimated quality, it would be seen by more customers and hence garner more reviews; the opposite would be true for products with low estimated quality. As Figure 4(a) shows, EB offers one way for products that "unfairly" receive low reviews to maintain relatively accurate estimated quality even with few reviews, but endogeneity could still influence the overall EB estimation procedure. As experiments on the scaled dataset show, low-rated products could fall below the threshold to be included in the training or evaluation process, and even if they were included, the ratings from these products may not reflect that product's true quality. In practice, a more sophisticated model would be dynamic: The platform creates a ratings system which induces certain types of products to get more ratings. These ratings then inform how the platform should update existing quality estimates for products. A ratings system that models this adaptive process would be invaluable if the end goal is real-world deployment, as a naive deployment of EB could suffer from the selection issues mentioned above.

\section{Conclusion}

In this paper we present an empirical Bayes framework for estimating the quality of products in an online marketplace. The key observation we made is that we could use data from multiple \textit{parallel} data sources to create a more descriptive model for individual products in that data. Our empirical Bayes approach is relatively simplistic, addresses the cold-start problem of many ratings systems, and performs better in terms of mean-squared error than a baseline, frequentist approach. However, our procedure tends to do worse on uncommon products in the population moreso than in the frequentist method, and could be vulnerable to selection problems in how the underlying data for the problem is generated. More work needs to be done on how endogenous data generation impacts ratings systems.

\bibliographystyle{ACM-Reference-Format}

\section{Introduction}

Online marketplaces that rely on user-generated ratings to judge the quality of listings on their platform, such as Amazon or Uber, suffer from a \textit{cold-start} problem, where a new listing is unable to be rated accurately because it has little to no review data. This impacts the ability for new listings with a single bad rating to gain notoriety, and also allows for bad listings that happen to receive a few good reviews to be unfairly promoted. Cold-start's consequences are well-documented in the context of recommender systems, where it is referred to as the \textit{new user problem} \cite{marlin2004collaborative}, and it is particularly problematic for online labour markets, where workers with little experience are unlikely to be hired \cite{pallais2014inefficient}.

Most online marketplaces calculate the estimated quality score of a product on the market using previous ratings that product has received, most commonly in the form of a sample mean. This leads to a problem in the context of cold-start; the first few ratings for a product could simply be the result of luck or malicious behaviour. For example, a high-quality product may have just gotten unlucky with a few bad ratings, or a poor-quality product may have found a way to "buy" a batch of fradulent reviews (perhaps by leaving high-quality ratings through sock-puppet accounts). As such, the naively estimated quality of the product from early ratings alone might not correspond to the actual ratings a product gets in the future. A better solution would be to be more lenient to new products with few ratings, or, better yet, consider information about how other similar products performed when they had only a few ratings.

We suggest a \textit{parametric empirical Bayes} (EB) algorithm to estimate the quality of a product, which takes into account more than just the past reviews of a product to generate a quality estimate. EB is a Bayesian estimation process; it assumes that there exists some prior distribution of quality from which products are drawn, and uses the individual ratings of the product to compute a posterior. Rather than use an uninformative prior or assume some outside knowledge about the parameters of the prior, EB fits this prior through empirical observations about the distribution of ratings in the overall population. This simple-to-use method exploits the fact that most online marketplaces have large amounts of \textit{parallel} data at the product level: there are many items on the market, each of which have their own ratings data. When a new product enters the market, we should be able to leverage our knowledge about similar products that already exist to temper our expectations of the quality of the new good. Using the average quality of each product in a population, we can fit a prior over what the quality of a new good in an existing population will be. We then treat any user reviews for that new good as updates to the prior distribution, using this information to present a quality estimate.

We test this approach on a dataset of Amazon reviews, comparing the quality of estimation to naively computing the sample mean (what we call the \textit{frequentist approach}), with a particular interest in how either method works in low data regimes. To control for potential selection issues in the data generation process, we also replicate this analysis on synthetic data. We find that for all datasets, the empirical Bayes approach has lower overall mean-squared error, with dramatic improvements on products with few ratings: On the Amazon dataset, we achieve an average 72\% reduction in mean-squared error when the EB algorithm sees a product with 10 or fewer reviews. However, EB also gives less accurate predictions on "outlier" products that have unusually high or low quality scores relative to the population, until enough ratings are received for the outlier to overcome EB's initial skepticism. We finish with a discussion of why we believe an implementation of our model in a real-world market would require modelling the ratings generation process as endogenous to the model, rather than simply being given as training data.

\section{Related Work}

Empirical Bayes methods have been well-studied and widely used in statistics literature since their introduction by Robbins~\cite{robbins1992empirical}, most notably for the method's applications in statistical decision theory~\cite{robbins1964empirical}. Empirical Bayes also has a long history of being used for statistical inference \cite{morris1983parametric,efron2001empirical,bastani2021efficient}; to our knowledge, our work is the first to use EB for statistical inference rating systems for online marketplaces. Ignatiadis and Wager~\cite{ignatiadis2019covariate} infer the quality of movies with empirical Bayes estimators when one has access to feature-level data for each movie in addition to ratings, but mainly emphasize the general minimax optimality bounds for their approach.

On the ratings system side of literature, user-generated reviews as a feedback system have become increasingly widespread in online platforms over the past two decades \cite{dellarocas2003digitization}. Empirical experiments have shown the importance of early ratings on a product's success on online marketplaces~\cite{cabral2010dynamics}, as well as the possible impacts that social influence can have on an item's success~\cite{salganik2006experimental,bolton2013engineering}. To investigate these effects, many empirical studies have implemented novel ratings system and analyzed their impacts: \citet{gaikwad2016boomerang} design an online labour marketplace where the raters' judgements have consequences for future transactions, while \citet{garg2021designing} assess how changing the language of the surveys presented to raters can drastically alter ratings scores. From a more theoretical, model-building perspective, \citet{garg2019designing} designed an optimal ratings system to recover the true quality of products in a \textit{binary} rating system where the rating can either be 0 (dislike) or 1 (like). Most related to our work, \citet{kokkodis2015reputation} use Bayesian methods and linear dynamical systems to predict the quality scores of individuals in online labour markets when those individuals participate in multiple different categories of work.

\section{Model and Method}

In this section, we develop a model to formalize our ratings problem. The key assumption of this model is that every product in an online market has a true quality score that is drawn from an underlying \textit{population distribution} of items, and that, with enough ratings data for an individual product, the estimated quality of that product resembles the true quality. Our goal will be to estimate the true quality of a product, even if there are not many ratings for it. We take a Bayesian approach: We will treat the population distribution as our prior, and the ratings-generation process for a single product as our data-generating process.

We assume we are given a dataset of products $R$, with each product having some number of 1-, 2-, 3-, 4-, and 5-star ratings. While EB is a statistical method that works for many distributions, for simplicity, we model each product $r \in R$ as generating ratings according to a multinomial distribution with event probability parameters $p_{1r}...p_{5r}$. Each product $r$ has $N_r$ reviews, with $r_i \leq N_r$ referring to the number of $i$-star reviews garnered by a product.

For each product, we model $(p_{1r},...p_{5r})$ as being drawn from a Dirichlet distribution with parameters $\alpha = (\alpha_1...\alpha_5)$, which represents a population that the products are being drawn from. Unlike a traditional Bayesian approach, in which the parameters of the prior are either set to be uninformative or given as hyperparameters, in parametric empirical Bayes, we fit $\alpha$ using population-level data. For each product $r$, we estimate the event probability parameter for an $i$-star review to be $\hat{p_{ir}} = r_i/N_r$. This reflects our assumption that, provided each product in the training dataset has enough reviews, the estimated event probability parameter resembles the true event probability parameter.

We use these estimates to calculate a maximum-likelihood estimate of $\alpha$. To compute MLEs $\hat{\alpha_1}...\hat{\alpha_5}$ from the set of probability parameter estimates $\{(\hat{p}_{1r}...\hat{p}_{5r})\}_{r \in R}$, we use an iterative method for calculating the maximum likelihood estimators of the Dirichlet distribution parameter~\cite{huang2005maximum}: If $\hat{\alpha_{t,i}}$ is the estimate for $\alpha_i$ at iteration $t$, the update rule is

\begin{align}
    \hat{\alpha}_{t+1,i} &= \psi^{-1}\left(\psi\left(\sum_{j=1}^5 \hat{\alpha_{t,j}}\right) + \frac{1}{N}\sum_{r \in R} \log(\hat{p_{ir}})\right),
\end{align}

where $\psi$ is the digamma function. We iterate until convergence is achieved, getting the prior parameter estimate $\hat{\alpha} = (\hat{\alpha}_1...\hat{\alpha}_5)$. To estimate the quality of a new product $d$ with observed number of $i$-star reviews $d_i$ for $i \in \{1...5\}$, we exploit conjugacy and find

\begin{align} \label{postupdate}
    \textrm{prob}(p_{1d}...p_{5d}|d_1,d_2...d_5) \sim \textrm{Dirichlet}(\hat{\alpha_1}+d_1...\hat{\alpha_5}+d_5)
\end{align}

We compute the posterior mean estimates $(\tilde{p_{1d}}...\tilde{p_{5d}})$ from this distribution as our empirical Bayes estimates of the event probability parameter of getting an $i$-star review for product $d$.

Throughout the next section, we contrast quality estimates derived from these posterior means with the \textit{frequentist approach} for estimating product quality, which we define here to simply be the sample mean of a product's existing ratings: If we have a new product $d$ with observed number of $i$-star reviews $d_i$ for $i \in \{1...5\}$, the frequentist approach estimate of $p_{id}$ is simply $d_i/\sum_jd_j$. This is equivalent to the maximum likelihood estimator in a frequentist setting, and is what many large online platforms, like Uber, use for calculating estimated quality scores~\cite{uber}.

\section{Experiments}

The primary goal of our experiments is to investigate how our empirical Bayes estimation method compares to traditional frequentist estimation. We are particularly interested in the performance of these estimators in low-data regimes, as well as identifying if there are any trade-offs between the two methods, and looking at specific examples of products that gain or lose significantly when moving from frequentist quality estimates to EB. We chose to use R to implement our experiments; all of the code and data for our experiments can be found at [\url{https://github.com/LEFTA98/empirical_bayes}], including code for generating the synthetic datasets.

For each of the datasets below, we split the users 60-40 into a train-test split. After training a prior using the training subset with the method described in Section 3, we carry out our analysis as follows: First, we filter out any products with fewer than 100 reviews, then cap any remaining products at exactly their 100 earliest reviews. We further split this set into a \textit{learning set} and \textit{evaluation set}, where the former contains the first 50 reviews for each test set product and the latter contains the last 50 reviews for each test set products. Let $r^{\textrm{learn}}_i$ ($r^{\textrm{eval}}_i$) refer to the number of $i$-star reviews for product $r$ in the learning set (evaluation set), and $N_r^{\textrm{learn}}$ ($N_r^{\textrm{eval}}$) be the total number of reviews for product $r$ in the learning set (evaluation set). While filtering out data with fewer than 100 data points seems counterintuitive to solving the cold start problem, we take this approach so that we have a reliable ground-truth estimate of what the quality of a product is through the evaluation dataset; we investigate cold-start in this context by limiting the number of ratings per user in the learning set the algorithm sees.

\subsection{Datasets}

We make use of a dataset of reviews for 71,982 products listed under the "Video Games" section on Amazon, sold on the platform from 1997 to 2018. We chose to use this dataset because of the quantity of data available, and because of its relative reliability: While the distribution of ratings among products in this dataset is heavily left-tailed (see Figure 1), it is actually more heterogeneous than most product categories on Amazon, with all average ratings from 1 to 5 being adequately represented. There were about 2,565,349 distinct reviews in this dataset, which is public and available online~\cite{jianmo}.

To investigate how our model works on differently distributed data, we also create synthetic datasets. We generate two synthetic datasets---the first assumes the true Dirichlet parameters to be $\alpha = (1,1,1,1,1)$, which induces a uniform prior, creating a population where the average quality is centered around 3 stars. It then draws a value $(p_1...p_5)$ from this prior to create a synthetic product, then draws from a Multinomial$(100, (p_1...p_5))$ distribution to generate 100 ratings for this product. We repeat this 10,000 times for a total of 1 million data points, and call this the \textit{uniform} dataset. The next dataset investigates what may happen if the data-generation process is endogeneous to the true quality of each product; low-quality products may be more likely to self-censor by exiting the market early or be deprioritized by the platform's search and ranking algorithms, and hence be less likely to generate reviews. We create a \textit{scaled} dataset which draws user parameters $(p_1...p_5)$ from a uniform prior as before, except now, the number of the trials in the multinomial ratings generation process is decided by a Poisson($\lambda$) random variable, where $\lambda$ is a rate hyperparameter that should be a function of the true quality of the product. For the purposes of this experiment we choose $\lambda = \frac{100}{3}\sum_{i=1}^5 ip_{i}$. This ensures that most products who are above-average quality will be above the 100-number cutoff for the test set, though there will be significantly less representation of lower-than-average products in our experiments; in practice, this should not change the distribution of ratings across products, but will significantly impact the availability of data for low-quality goods.

After splitting each dataset into train and test sets, we use the training data to fit a Dirichlet prior for each dataset, as per Section 3, filtering out from the training set any products with fewer than 20 reviews. Histograms of the average rating of each good in each dataset are shown in Figure 1 for products that have 20 or more reviews (and hence would not be filtered out from the experiment).

\begin{figure}
  \begin{center}
    \includegraphics[scale=0.25]{figures/f1.png}
  \end{center}
  \caption{Histograms showing distribution of average ratings of products with 20 or more reviews for different datasets. Note the heavy left-tailed skew for the Amazon dataset. Ratings for products in the scaled synthetic dataset were generated at a rate proportional to the true quality of the product. Note that this did not change the distribution of ratings of products in the scaled dataset compared to the uniformly generated synthetic dataset, though it does affect availability of ratings data for low-quality goods. }
\end{figure}

\subsection{Over-time comparison of EB and frequentist}

The main advantage that we find the EB model to have over the frequentist approach is in how accurately it predicts the true quality of a product based on very few datapoints. We find that, when looking at the population-level mean-squared error, EB performs significantly better than the frequentist approach, with the largest gains being made in low-data regimes where there are few training examples for each product.

Our first experiment looks at how accurately the empirical Bayes posterior mean can estimate the true quality of a product when compared against the frequentist approach. We assume that for each product $r$ in the test set of products, the proportion of $i$-star ratings it gets in the evaluation set is equivalent to the true probability parameter; that is, we assume $p_{ir} = r^{\textrm{eval}}_i/N^{\textrm{eval}}_i$. For example, if 10 out of the 50 product reviews for product $r$ in the evaluation set are 4-star reviews, we assume that the true probability that a review is 4 stars for $r$ is $1/5$. Given a set of estimators $\{\hat{\theta}_{ir}\}_{i \in \{1...5\}, r \in R}$, we define the \textit{mean-squared error} to be $\frac{1}{|R|} \sum_{r \in R}\sum_{i=1}^5 (\hat{\theta}_{ir} - p_{ir})^2$. Also of note for our later experiments will be the \textit{per-product mean-squared error}, which is computed for a given product $r$ and given by $\sum_{i=1}^5 (\hat{\theta}_{ir} - p_{ir})^2$, and the \textit{estimated quality} of a given product $r$, calculated as $\sum_{i=1}^5 i\hat{\theta}_{ir}$.

We compare the posterior mean calculated from equation \eqref{postupdate} with the frequentist approach, which computes $r^{\textrm{learn}}_i/N^{\textrm{learn}}_i$ as the estimate for the $i$th event probability parameter for product $r$ and does not use data from the training set. Figure 2 shows our observations of this comparison, where we vary the number of reviews that each product in the learning set gives to the model, ordered from oldest reviews first to newest reviews last. In all datasets, we see that our EB estimator achieves a lower mean-squared error than the frequentist approach at all learning window sizes, with the greatest improvements made when the number of training examples seen is low. In particular, the mean-squared error for EB dips below 0.1 for all datasets after seeing just 3 learning examples, compared to 12 learning examples for the frequentist approach on the Amazon dataset. Note the MSE for both estimates approach each other as the number of reviews increases; this fits the natural Bayesian intuition of the prior being overwhelmed by data as the number of learning examples increases.

\begin{figure}
  \begin{center}
    \includegraphics[scale=0.22]{figures/f2.png}
  \end{center}
  \caption{Comparison of mean-squared error of empirical Bayes versus frequentist quality estimation, indexed by number of learning examples seen. The y-axis represents the mean-squared error. In all datasets, EB's gains over the frequentist approach are greatest in low-data regimes where the cold-start problem traditionally exists; after that, both methods converge to the same estimates. }
\end{figure}

Figure 2 shows the advantages of EB in cold-start scenarios: Empirical Bayes performs better than frequentist in low-data regimes. However, Empirical Bayes does not perform well across all products. This is seen in Figure 3, which plots the per-product mean squared error, stratified across the "true quality" of the product $\sum_{i=1}^5 ir^{\textrm{eval}}_i/N_r$. We observe that, in settings with few learning examples, EB gives good quality estimates for products with true ratings that were commonly present in the training data of the EB prior---in the case of the Amazon dataset, this value is roughly around 4 stars. However, products with true quality ratings that were not common in the population, such as 1-star products in the Amazon dataset, did better under the frequentist procedure when there were few learning examples. This suggests that the empirical Bayes estimator performs better on common products and does worse on outliers, while the frequentist estimator performs similarly on all products. Also of note are the results for the scaled dataset: Due to the lower number of ratings for low-quality goods, we have no information on products with a rounded quality score of less than 2, as many low-quality goods had an insufficient quantity of reviews to meet the test set cutoff of 100 reviews or more. This could imply an underrepresentation of low-quality goods in the Amazon dataset: if the true underlying data generation process for the Amazon dataset was dependent on the true quality of each product, as it was in the scaled dataset, then truly low-quality Amazon products would have less ratings and might not be included in fitting the EB algorithm.

\begin{figure*}
  \begin{center}
    \includegraphics[scale=0.3]{figures/f3wide.png}
  \end{center}
  \caption{Comparison of empirical Bayes versus frequentist quality estimation, stratified by true quality of the product, rounded to the nearest multiple of 0.5. The EB estimation error is lowest around the most common true quality scores for that dataset, but the frequentist approach beats EB on products with uncommon true quality scores relative to the population. The columns show the number of learning examples used.}
\end{figure*}

\begin{figure*}
    \begin{center}
    \includegraphics[scale=0.26]{figures/ebgoodfig.png}
    \includegraphics[scale=0.26]{figures/ebbadfig.png}
    \caption{Figures 4(a) (left) and 4(b) (right): Estimated quality of individual Amazon products indexed by number of learning examples. 4(a): the estimated quality of the product for which the one-datapoint frequentist estimator was furthest from the true average. 4(b): the estimated quality of the product for which the difference between the 50-datapoint EB estimator and ground truth was furthest off from the difference between the 50-datapoint frequentist estimator and ground truth. The straight line represents the true average, while the black dots represent individual ratings. EB does well for products that get bad ratings but improve over time, but for products with an uncommon true average, EB is eclipsed by frequentist estimation.}
    \end{center}
    \label{fig:my_label}
\end{figure*}

\subsection{Investigating individual products most impacted by empirical Bayes}

In this subsection, we analyze individual products in the Amazon dataset with estimated qualities that differ the most when swapping out the frequentist approach for the EB estimator. Figure 4(a) shows the estimated quality, indexed by number of learning examples seen, for the product with the largest possible difference between its true average score and the frequentist approach's estimated quality when using only one learning example. This particular product benefited greatly from EB, as it received many poor ratings early on, but gradually improved: When there were few data points, EB was willing to put more weight into the prediction that the product was close to the average population quality, which ended up being indicative of the good's true quality.

Conversely, Figure 4(b) shows a similar graph to 4(a), but for product that benefited the most after 50 learning examples from using the frequentist approach instead of EB. We quantify this by taking the good for which (difference between ground-truth, EB estimate) - (difference between ground-truth, frequentist estimate) was largest. This product received mostly 1-star reviews, though it had a few good reviews at the beginning. Despite the overwhelmingly negative feedback from ratings, there were still enough 5-star ratings for this product so that the prior from empirical Bayes was still not overwhelmed after 50 learning examples. Note that our analysis from Section 4.2 suggests that there are far more items within the population that resemble the product in Figure 4(a), rather than the product in Figure 4(b). If this were not the case, then the fitted population prior would have instead had more probability mass towards lower-quality goods, meaning EB would have been more likely to believe goods were low-quality when operating off few datapoints, and so the EB estimate for Figure 4(b) would be lower. Figure 4 highlights a key limitation of our relatively simplistic EB model: Depending on which is more common in the underlying population, EB can either correct for products that ranked unusually low for their first few reviews, or for products that ranked unusually high for their first few reviews, but not for both at the same time.

\section{Future work}

Many open directions remain from this study. EB could be used as an approach to model \textit{transfer learning} in online marketplaces, where one tries to estimate the quality of a worker or product in a new market based on their past performance in previous market(s), such as in \cite{kokkodis2015reputation}. We believe, however, that the potential endogeneity of data generation mentioned in Section 4 is one of the most important aspects of this problem to work on. Because online platforms usually give highly-rated goods more exposure, it would be reasonable to assume that ratings are generated adaptively in response to the currently estimated quality of a product. If the product has a high estimated quality, it would be seen by more customers and hence garner more reviews; the opposite would be true for products with low estimated quality. As Figure 4(a) shows, EB offers one way for products that "unfairly" receive low reviews to maintain relatively accurate estimated quality even with few reviews, but endogeneity could still influence the overall EB estimation procedure. As experiments on the scaled dataset show, low-rated products could fall below the threshold to be included in the training or evaluation process, and even if they were included, the ratings from these products may not reflect that product's true quality. In practice, a more sophisticated model would be dynamic: The platform creates a ratings system which induces certain types of products to get more ratings. These ratings then inform how the platform should update existing quality estimates for products. A ratings system that models this adaptive process would be invaluable if the end goal is real-world deployment, as a naive deployment of EB could suffer from the selection issues mentioned above.

\section{Conclusion}

In this paper we present an empirical Bayes framework for estimating the quality of products in an online marketplace. The key observation we made is that we could use data from multiple \textit{parallel} data sources to create a more descriptive model for individual products in that data. Our empirical Bayes approach is relatively simplistic, addresses the cold-start problem of many ratings systems, and performs better in terms of mean-squared error than a baseline, frequentist approach. However, our procedure tends to do worse on uncommon products in the population moreso than in the frequentist method, and could be vulnerable to selection problems in how the underlying data for the problem is generated. More work needs to be done on how endogenous data generation impacts ratings systems.

\bibliographystyle{ACM-Reference-Format}

redpajama_set_name: RedPajamaArXiv


Our quick responsive surface probe ("leaf" or "paddle sensor") is ideally suited for the accurate measurements of various surfaces.
This popular B+B surface probe, type K, comes with green helical cable and a green thermocouple connector according to DIN EN 60584. It is ideally suited for quick measurements on various surfaces and in areas that are difficult to access. The extremely thin thermocouple sensor at the measuring tip ensures a very fast response time.


Powerful electric grass trimmer and lawn edger!
The Flymo Contour 500E Electric Grass Trimmer & Lawn Edger offers a quick and easy way to trim and edge the contours of your lawn.
The Contour 500E is equipped with a powerful 500W motor and three operating modes that trim, edge and shrub-shear your lawn. With its 25cm Dual Auto feed system that automatically feeds the line, you no longer have to leave your trimming when you need new line.
With its adjustable handle and lightweight construction (only 3.1kg), the Flymo Contour 500E will make light work of any gardening task. Its 10 metre mains cable offers great freedom and can be stored integrally. A plant-guard on the Contour 500E will allow you to cut around the base of shrubs and plants without fear of damaging them.


With incoming manager Antonio Conte preferring either a 3-5-2 or 4-2-4 formation, it is important Chelsea upgrade in the striker department with Costa our only consistent and reliable front man.
It is likely that Falcao, Pato and Remy will leave us this summer and therefore there is also a problem of depth in the striker department, one that should be solved with promoting youth team strikers. However there is still the task of finding a world class striker to accompany Costa up top, assuming Hazard doesn't join him.
Chelsea have recently been linked with former player Romelu Lukaku, the striker who has impressed this year in an otherwise poor season for Everton. Whilst there are many positives to Lukaku's gameplay (as witnessed when we played Everton in the FA cup), there are questions that need to be answered about this whether this supposed transfer would be a good idea for Chelsea.
Firstly, it has been reported that it would take £65 million for Everton to sell their main man, and for this fee, Chelsea would be better off exploring different avenues.
For £65 million, Chelsea could buy the fantastic all-round central midfielder Radja Nainggolan, (supposedly around £30-35 million) and a good central defender such as Koulibaly who would cost a reported £20 million. This would give us two players we urgently need to boost our underperforming squad and leave us with money left over for other players we may need.
Yes, we need a striker and he would likely be the most expensive acquisition this summer for Chelsea, however there are far better strikers available for less than the outrageous fee for Lukaku.
Higuain and Cavani are both cheaper and better strikers and although they are older than Lukaku, 28 and 29 respectively, they provide a definite improvement to our squad,whereas Lukaku does not provide any upgrade on our current main striker Costa.
When comparing these 4 strikers over the past two seasons in their respective domestic leagues (stats from whoscored), it is clear that Lukaku is not comparable to the others in terms of quality.
As seen above, Lukaku has the worst by far over the last two seasons in the league when coming to goals and assists. Higuain is by far the most prolific and that is why he should be the target that Chelsea pursue.
Whilst it is true that Cavani and Costa play for greater teams, they are not the main men in their teams (Ibrahimovic and Hazard respectively) unlike Lukaku who is relied upon heavily by Everton to score and assist the goals. This gives him an advantage as players will look to find him more regularly compared to the others.
His attitude of needing to be the number one choice is not suited to a big club as players will always be transferred in to bring competition and improve players, and if Lukaku cannot deal with this then he should not be considered an option for Chelsea.
Yet it can be said that Mourinho had a similar opinion of Kevin de Bruyne who has now turned out to be one the most creative number 10's in the world, and therefore what Mourinho said must be taken with a pinch of salt.
Finally, bringing Lukaku back may be seen as bad for Chelsea's youth development. This is because Lukaku is only 23, and therefore bringing him back will block the path for our young strikers for many years.
By purchasing an older player it will mean that the young players will still be able to make their mark in a few years when the older striker will become less effective, which would not be possible with Lukaku.
I would much rather see any of Solanke, Traore or Abraham given the chance as our number 3 and 4 strikers behind Costa and Higuain/Cavani than the costly and moody Lukaku.
To conclude, Lukaku is not worth the money, doesn't have the quality and and has the wrong attitude to provide Chelsea with a world-class striker to accompany Diego Costa. Feel free to leave comments if you agree/disagree.
Next articleWill Romelu Lukaku re-join Chelsea this summer?


text:
Location : University of Southampton
Fluid Structure Interaction Design Development of Passive Adaptive Composite International Moth Foil
Author(s): J. Banks; L. Marimon Giovannetti; M. Ledri; S.R. Turnock; S.W. Boyd
Location: University of Southampton
Keyword(s): fluid dynamics; foil; hydrofoils
The International Moth is a single-handed ultra-lightweight foiling development class boat, and it fol- lows open class rules. Therefore, the designer and builder have full liberty to develop and produce the fastest boat [1]. It is possible to adapt the internal structure of the fixed foil to achieve a tailored twist angle for a given load. Exploring the possibility of using Passive Adaptive Composite (PAC) on the moth hydrofoil to control its pitch angle enables the boat to achieve a stable flight in a wide range of weather conditions whilst reducing the induced drag, passively decreasing the angle of attack in increased boat speed. Using PAC in a multi-element foil, such as the International Moth one, will allow the structure to achieve a constant lift force with speeds higher than the design take-off speed with less need to con- stantly modifying the rear foil section. Toward the development of a PAC moth fixed foil, experimental and numerical results for a single element aerofoil, able to achieve a linear decrease in lift coefficient with increase in wind speed, are presented and discussed. The results present the aero-elastic response of the foil explaining the complexity involved in fluid-structure interaction problems.
Hydrofoiling Catamaran Experimental Research Platform
Author(s): J. Banks; S.W. Boyd; A. Ayan; A. Vose; S. Jones; F. Hayes; J. Diamond
Keyword(s): catamaran; hydrodynamic lift; hydrofoils; foil
This paper outlines the development of a hydro-foiling catamaran experimental research platform. The platform was designed to allow the configuration to be easily adjusted to assess the effects of various parameters on the performance and stability of the craft. In order to determine the performance of the craft, a data acquisition system was developed to record wind, speed, heading and IMU data. A hydro- foiling velocity predicition program was written to provide a comparison tool between the physics and data collected on the water.
Development of an America's Cup 45 Tacking Simulator
Author(s): A. K. Lidtke; L. Marimon Giovannetti; A. Sampson; M. Vitti; D.J. Taunton
Keyword(s): sails; simulation; strength; stress; velocity prediction program (VPP); wing section
This paper describes the development of an AC45 simulator conducted as a student Master's project at the University of Southampton. The main aim was to be able to asses and improve the tacking skills of the helm and the crew through systematic training. The physical interface of the simulator replicates the seating position of the helmsman and the main trimmer and the graphical representation provides the users with visual cues of the simulated boat, boundaries and marks for a sample race course. The theoretical model uses hydrodynamic manoeuvring coefficients based on empirical formulae and experimental data. The aerodynamic forces are pre-calculated using a full-scale RANS CFD simulation. The accuracy of the model is verified against the AC45 racing tracking data to ensure that the speed loss during a tack, experienced by the users of the simulator, is as close to reality as possible. The ultimate aim of the project was to study the potential of the simulator to assess and train the crews, improving their skill in tacking the boat effectively. This has been done by examining the performance of two groups of users over a series of practice sessions. The simulator could be potentially used for training the helmsmen of the Youth America's Cup Red-Bull teams, which have limited budgets, training days and sailing experience compared to the professional AC sailors.
An Experimental Investigation of Slamming on Ocean Racing Yachts
Author(s): Philip A. Wilson; Paolo Manganelli
Keyword(s): beam; performance assessment; slamming; slamming loads; waterline length; impact & slamming loads
Groupe Finot Naval Architects and the School of Engineering Sciences, Ship Science of the University of Southampton have started a joint research project to carry out an experimental investigation concerning the effects of slamming on offshore sailing yachts. A reliable autonomous data acquisition system was designed that allowed measurements to be taken during long offshore races. The details of the design and implementation of this system are presented together with some sample results from the first measurement campaigns.
An Investigation of the Structural Dynamics of a Racing Yacht
Author(s): Frederic Louarn; Pandeli Temarel
Keyword(s): finite element analysis; model test data; structural loads
The dynamic behaviour of a WOR 60 is investigated using three dimensional hydroelasticity theory. Global structural responses (e.g. stresses) in waves are obtained corresponding to the upright as well as to the more realistic heeled sailing configurations, revealing the connection between the ballast keel and the hull as being a critical area of the structure. For the "dry hull" analysis, a global finite element model has been developed, incorporating the hull and deck shell, the internal structure, the ballast keel and the rig together with rigging loads. The modular nature of the model has been used to assess the relative influence of each of the aforementioned components upon the required characteristic dynamic properties (e.g. natural frequencies and principal mode shapes). Regarding the "wet hull" analysis, a three dimensional Green's function technique, using pulsating sources distributed over the wetted surface, provides a numerical solution to the case of the yacht sailing in regular waves at arbitrary heading. Principal coordinates for the rigid body motions and flexible distortions of interest are evaluated and the latter are used to obtain the dynamic stresses in waves using modal summation. This paper will describe the modelling techniques used and discuss the applicability I limitations of hydroelasticity theory regarding this type of structures in the light of the results obtained for the upright and heeled operational conditions, as well as from the point of view of design aspects such as "L" and "T" keel configurations. The ABS design criteria will provide a practical reference for comparing the results from the dynamic analysis.


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text:
Q: List View HTML Static vs Dynamic I'm trying to dynamically create HTML lists using some random JSON data
The code is -

Lists

AJAX List View

When I run this code it views something like this -

But when I try to do the above in a static manner by writing every UL & OL it runs as I need.

Header Libs -
<link rel="stylesheet" href="http://code.jquery.com/mobile/1.4.5/jquery.mobile-1.4.5.min.css">

A: did the data-role="collapsible" & data-role="listview" is attribute for jQueryMobile objects?
if yes, after ajax loaded successfully, you need to re-draw them to make sure they are compiled with right appearances.
Refers from jQueryMobile api documentation, you can draw the collapsible using this:
$( ".selector" ).collapsible();

and this is for listview drawing init:
$( "#mylist" ).listview();

For your script, you need add those two initializer just like this:
var str;
var xmlhttp = new XMLHttpRequest();
xmlhttp.onreadystatechange = function() {
    if (xmlhttp.readyState == 4 && xmlhttp.status == 200) {
        str = xmlhttp.responseText;
        str = JSON.parse(str);
        var q = "";
        for (i = 0; i < str.length; i++) {
            q += "

" + str[i].title + "
";
            q += "

Details: " + str[i].duration + "

Price: " + str[i].price + "

";
            q += "
";
        }
        document.getElementById('list').innerHTML = q;
    }

    $('div[data-role="collapsible"]').collapsible();
    $('ul[data-role="listview"]').listview();
};
xmlhttp.open("GET", "http://phonegappro.esy.es/test/json.php", true);
xmlhttp.send();

Pardon me for my bad english :)

redpajama_set_name: RedPajamaStackExchange


text:
Q: Animated gif during script processing I have a script called notify_me.php which I run like so:
script type="text/javascript">
    //Run notify_me.php script
    $(document).ready(function(){
      $("#submit").click(function(){
        var d = $('form').serialize();
        $.get('php/notify_me.php',d,function(data){
           $(".container").html(data);
        });
      });
    });
</script>

and I would like to show a animated loading .gif until the script is printed. The code for that is :

   Fetching your flight prices...

How can I write a function that shows the .search_load class during the processing of notify_me.php. The .search_load class should also be shown in the .container div.
Tried some different ways with append(); and appendTo(); but can't seem to get it working.
Appreciate your help on this!
EDIT: I got the .search_load div to show the first time I hit the #submit. The second time it doesn't show att all. This is the problem I'm trying to solve. Any ideas?!
SOLUTION: Guys, I solved it by looking in to @Rohan's link. Check out below. Thank you all!
$(document).ready(function(){
   $("#submit").click(function(){
     $('#info').show();
     $('html,body').animate({scrollTop: $("#info").offset().top},'slow');
     $('.container').after('

');
     var d = $('form').serialize();
     $.get('php/notify_me.php',d,function(data){
       $(".container").html(data);
       $('.search_load').hide();
     });
   });
});

A: $(document).ready(function(){
    $('.search_load').hide();
    $("#submit").click(function(){
        var d = $('form').serialize();
        $('.search_load').show();
        $.get('php/notify_me.php',d,function(data){
        $('.search_load').hide();
            $(".container").html(data);
        });
    });
});

You can also hide the div with CSS, so you can remove the line #2:  $('.search_load').hide();

A: Steps:

*

*Make your loading div hidden

*When loading starts, display it using .show() and modifying the CSS so that its placement is correct

*OnLoaded -> div.hide()

Refer to this: How to show waiting message during sync ajax call in browser

A: jQuery(document).ready(function($) {
  $("#submit").click(function(){
    $(".search_load").show();
    var d = $('form').serialize();
    $.get('php/notify_me.php', d, function(data) {
       $(".container").html(data);
       $(".search_load").hide();
    });
  });
});

A: try this:
$('div.search_load').hide();
$('#submit').click(function() {
    $('div.search_load').show();
    var d = $('form').serialize();
    $.get('form.php', d,
    function(data) {
        $('div.search_load').hide();
        $('.container').html(data);
    },
    'html');
    return false;
});

A: Try This:
Javascript:

HTML Changes:

    Fetching your flight prices...

Hope this will work.


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