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Linear discriminant analysis is a widely used method for classification. However, the high dimensionality of predictors combined with small sample sizes often results in large classification errors. To address this challenge, it is crucial…

Numerous statistics have been proposed for the measure of offensive ability in major league baseball. While some of these measures may offer moderate predictive power in certain situations, it is unclear which simple offensive metrics are…

Domain generalization aims at training machine learning models to perform robustly across different and unseen domains. Several recent methods use multiple datasets to train models to extract domain-invariant features, hoping to generalize…

Linear dimensionality reduction methods are a cornerstone of analyzing high dimensional data, due to their simple geometric interpretations and typically attractive computational properties. These methods capture many data features of…

Despite the prominence of neural network approaches in the field of recommender systems, simple methods such as matrix factorization with quadratic loss are still used in industry for several reasons. These models can be trained with…

Many machine learning applications deal with high dimensional data. To make computations feasible and learning more efficient, it is often desirable to reduce the dimensionality of the input variables by finding linear combinations of the…

In the high-stakes world of baseball, every nuance of a pitcher's mechanics holds the key to maximizing performance and minimizing runs. Traditional analysis methods often rely on pre-recorded offline numerical data, hindering their…

In most popular sports leagues, like the MLB, NBA, and NFL, none of the commonly used statistics take into account the strengths of the opponents a player faces. One of the main reasons for this is the conventional belief that a player's…

Forecast combinations have been widely applied in the last few decades to improve forecasting. Estimating optimal weights that can outperform simple averages is not always an easy task. In recent years, the idea of using time series…

In this paper, we study randomized reduction methods, which reduce high-dimensional features into low-dimensional space by randomized methods (e.g., random projection, random hashing), for large-scale high-dimensional classification.…

Many probabilistic models that have an intractable normalizing constant may be extended to contain covariates. Since the evaluation of the exact likelihood is difficult or even impossible for these models, score matching was proposed to…

Domain generalization aims to learn invariance across multiple training domains, thereby enhancing generalization against out-of-distribution data. While gradient or representation matching algorithms have achieved remarkable success, these…

The use of statistical modeling in baseball has received substantial attention recently in both the media and academic community. We focus on a relatively under-explored topic: the use of statistical models for the analysis of fielding…

As an alternative to variable selection or shrinkage in high dimensional regression, we propose to randomly compress the predictors prior to analysis. This dramatically reduces storage and computational bottlenecks, performing well when the…

Dimension reduction plays a pivotal role in analysing high-dimensional data. However, observations with missing values present serious difficulties in directly applying standard dimension reduction techniques. As a large number of dimension…

Domain generalization methods aim to learn models robust to domain shift with data from a limited number of source domains and without access to target domain samples during training. Popular domain alignment methods for domain…

We provide a remedy for two concerns that have dogged the use of principal components in regression: (i) principal components are computed from the predictors alone and do not make apparent use of the response, and (ii) principal components…

The distribution shifts between training and test data typically undermine the performance of models. In recent years, lots of work pays attention to domain generalization (DG) where distribution shifts exist, and target data are unseen.…

Estimation of density functions supported on general domains arises when the data is naturally restricted to a proper subset of the real space. This problem is complicated by typically intractable normalizing constants. Score matching…

In clinical settings, we often face the challenge of building prediction models based on small observational data sets. For example, such a data set might be from a medical center in a multi-center study. Differences between centers might…