In the quantitative analysis of competitive sports, a fundamental task is to estimate the skills of the different agents ('players') involved in a given competition based on the outcome of pairwise comparisons ('matches') between said players, often in an online setting. Skill estimation facilitates the prediction of various relevant outcomes of subsequent matches, which can then be applied towards high-level decision-making for the competition, including player seeding, fair team matching, and more. There are several established approaches to the task of skill estimation, including among others the Bradley-Terry model (Bradley and Terry, 1952), the Elo rating system (Elo, 1978), the Glicko rating system (Glickman, 1999), and TrueSkill (Herbrich et al., 2006) each with various levels of complexity and varying degrees of statistical motivation. Skill rating is of paramount importance in the world of competitive sports as it serves as a foundational tool for assessing and comparing the abilities of players and how they vary over time. By accurately quantifying skill levels, skill rating systems enable fair and balanced competition, inform strategic decision-making, and enhance the overall sporting level.

Statistical machine learning models have been increasingly used in fully or partially automatized data analysis processes and artificial intelligence applications (Rudin, 2019). The automatizing of decisions impacting the society inspire a parallel effort to develop methods to identify the factors impacting specific decisions. The heightened scrutiny on the way statistical models now operate at a large scale and at a fast pace has led to a renewed interest in statistical diagnostics such as the influence function (Cook and Weisberg, 1982; Koh and Liang, 2017; Schioppa et al., 2022; Louvet et al., 2022). The influence function or curve of a statistical estimator has been proposed to measure the sensitivity of the estimator to individual datapoints. Computing the influence of a particular datapoint boils down to computing an inverse-Hessian-vector product. Due to a greater focus on least-squares-type estimator with small samples, the computational aspects have received relatively little attention until recently (Koh and Liang, 2017; Schioppa et al., 2022), while the statistical aspects have mainly focused on large sample classical asymptotics (Rousseeuw et al., 2011; Avella-Medina, 2017). The statistical analysis of influence functions for generalized linear models presents several challenges.

Its efficiency strongly depends on the choice of the proposal. Self-learning Monte Carlo (SLMC) methods are recently proposed to accelerate Markov chain Among recent advances in machine learning, a general Monte Carlo (MCMC) methods using a machine method called the self-learning Monte Carlo (SLMC) learning model. With latent generative models, method (Liu et al., 2017) was introduced to accelerate SLMC methods realize efficient Monte Carlo updates MCMC simulations by an automated proposal with a machine with less autocorrelation. However, SLMC learning model and has been applied to various problems methods are difficult to directly apply to multimodal (Xu et al., 2017; Shen et al., 2018). In particular, distributions for which training data are a latent generative model realizes efficient global update difficult to obtain. To solve the limitation, we propose through the obtained information-rich latent representation "parallel adaptive annealing," which makes (Huang & Wang, 2017; Albergo et al., 2019; Monroe & SLMC methods directly apply to multimodal distributions Shen, 2022; Tanaka & Tomiya, 2017). Although powerful, with a gradually trained proposal while the performance of SLMC simulation strongly depends annealing target distribution. Parallel adaptive annealing on an automated proposal with machine learning models is based on (i) sequential learning with and the quality of training data to train the proposal. For annealing to inherit and update the model parameters, example, it is challenging to directly use SLMC for multimodal (ii) adaptive annealing to automatically detect distributions because obtaining accurate training data under-learning, and (iii) parallel annealing to covering all modes is difficult.

Numerical approximations of partial differential equations (PDEs) are routinely employed to formulate the solution of physics, engineering and mathematical problems involving functions of several variables, such as the propagation of heat or sound, fluid flow, elasticity, electrostatics, electrodynamics, and more. While this has led to solving many complex phenomena, there are some limitations. Conventional approaches such as Finite Element Methods (FEMs) and Finite Differential Methods (FDMs) require considerable time and are computationally expensive. In contrast, data driven machine learning-based methods such as neural networks provide a faster, fairly accurate alternative, and have certain advantages such as discretization invariance and resolution invariance. This article aims to provide a comprehensive insight into how data-driven approaches can complement conventional techniques to solve engineering and physics problems, while also noting some of the major pitfalls of machine learning-based approaches. Furthermore, we highlight, a novel and fast machine learning-based approach (~1000x) to learning the solution operator of a PDE operator learning. We will note how these new computational approaches can bring immense advantages in tackling many problems in fundamental and applied physics.

In multivariate time series systems, key insights can be obtained by discovering lead-lag relationships inherent in the data, which refer to the dependence between two time series shifted in time relative to one another, and which can be leveraged for the purposes of control, forecasting or clustering. We develop a clustering-driven methodology for robust detection of lead-lag relationships in lagged multi-factor models. Within our framework, the envisioned pipeline takes as input a set of time series, and creates an enlarged universe of extracted subsequence time series from each input time series, via a sliding window approach. This is then followed by an application of various clustering techniques, (such as k-means++ and spectral clustering), employing a variety of pairwise similarity measures, including nonlinear ones. Once the clusters have been extracted, lead-lag estimates across clusters are robustly aggregated to enhance the identification of the consistent relationships in the original universe. We establish connections to the multireference alignment problem for both the homogeneous and heterogeneous settings. Since multivariate time series are ubiquitous in a wide range of domains, we demonstrate that our method is not only able to robustly detect lead-lag relationships in financial markets, but can also yield insightful results when applied to an environmental data set.

In real-world scenarios like traffic and energy, massive time-series data with missing values and noises are widely observed, even sampled irregularly. While many imputation methods have been proposed, most of them work with a local horizon, which means models are trained by splitting the long sequence into batches of fit-sized patches. This local horizon can make models ignore global trends or periodic patterns. More importantly, almost all methods assume the observations are sampled at regular time stamps, and fail to handle complex irregular sampled time series arising from different applications. Thirdly, most existing methods are learned in an offline manner. Thus, it is not suitable for many applications with fast-arriving streaming data. To overcome these limitations, we propose BayOTIDE: Bayesian Online Multivariate Time series Imputation with functional decomposition. We treat the multivariate time series as the weighted combination of groups of low-rank temporal factors with different patterns. We apply a group of Gaussian Processes (GPs) with different kernels as functional priors to fit the factors. For computational efficiency, we further convert the GPs into a state-space prior by constructing an equivalent stochastic differential equation (SDE), and developing a scalable algorithm for online inference. The proposed method can not only handle imputation over arbitrary time stamps, but also offer uncertainty quantification and interpretability for the downstream application. We evaluate our method on both synthetic and real-world datasets.

The key assumption underlying linear Markov Decision Processes (MDPs) is that the learner has access to a known feature map $\phi(x, a)$ that maps state-action pairs to $d$-dimensional vectors, and that the rewards and transitions are linear functions in this representation. But where do these features come from? In the absence of expert domain knowledge, a tempting strategy is to use the ``kitchen sink" approach and hope that the true features are included in a much larger set of potential features. In this paper we revisit linear MDPs from the perspective of feature selection. In a $k$-sparse linear MDP, there is an unknown subset $S \subset [d]$ of size $k$ containing all the relevant features, and the goal is to learn a near-optimal policy in only poly$(k,\log d)$ interactions with the environment. Our main result is the first polynomial-time algorithm for this problem. In contrast, earlier works either made prohibitively strong assumptions that obviated the need for exploration, or required solving computationally intractable optimization problems. Along the way we introduce the notion of an emulator: a succinct approximate representation of the transitions that suffices for computing certain Bellman backups. Since linear MDPs are a non-parametric model, it is not even obvious whether polynomial-sized emulators exist. We show that they do exist and can be computed efficiently via convex programming. As a corollary of our main result, we give an algorithm for learning a near-optimal policy in block MDPs whose decoding function is a low-depth decision tree; the algorithm runs in quasi-polynomial time and takes a polynomial number of samples. This can be seen as a reinforcement learning analogue of classic results in computational learning theory. Furthermore, it gives a natural model where improving the sample complexity via representation learning is computationally feasible.

Abstract--Anomalies in the domain of autonomous driving are a major hindrance to the large-scale deployment of autonomous vehicles. In this work, we focus on high-resolution camera data from urban scenes that include anomalies of various types and sizes. Based on a Variational Autoencoder, we condition its latent space to classify samples as either normal data or anomalies. In order to emphasize especially small anomalies, we perform experiments where we provide the VAE with a discrepancy map as an additional input, evaluating its impact on the detection performance. Our method separates normal data and anomalies into isolated clusters while still reconstructing high-quality images, leading to meaningful latent representations.

Severe acute respiratory disease SARS-CoV-2 has had a profound impact on public health systems and healthcare emergency response especially with respect to making decisions on the most effective measures to be taken at any given time. As demonstrated throughout the last three years with COVID-19, the prediction of the number of positive cases can be an effective way to facilitate decision-making. However, the limited availability of data and the highly dynamic and uncertain nature of the virus transmissibility makes this task very challenging. Aiming at investigating these challenges and in order to address this problem, this work studies data-driven (learning, statistical) methods for incrementally training models to adapt to these nonstationary conditions. An extensive empirical study is conducted to examine various characteristics, such as, performance analysis on a per virus wave basis, feature extraction, "lookback" window size, memory size, all for next-, 7-, and 14-day forecasting tasks. We demonstrate that the incremental learning framework can successfully address the aforementioned challenges and perform well during outbreaks, providing accurate predictions.

In conventional statistical and machine learning methods, it is typically assumed that the test data are identically distributed with the training data. However, this assumption does not always hold, especially in applications where the target population are not well-represented in the training data. This is a notable issue in health-related studies, where specific ethnic populations may be underrepresented, posing a significant challenge for researchers aiming to make statistical inferences about these minority groups. In this work, we present a novel approach to addressing this challenge in linear regression models. We organize the model parameters for all the sub-populations into a tensor. By studying a structured tensor completion problem, we can achieve robust domain generalization, i.e., learning about sub-populations with limited or no available data. Our method novelly leverages the structure of group labels and it can produce more reliable and interpretable generalization results. We establish rigorous theoretical guarantees for the proposed method and demonstrate its minimax optimality. To validate the effectiveness of our approach, we conduct extensive numerical experiments and a real data study focused on education level prediction for multiple ethnic groups, comparing our results with those obtained using other existing methods.