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In overparameterized logistic regression, gradient descent (GD) iterates diverge in norm while converging in direction to the maximum $\ell_2$-margin solution -- a phenomenon known as the implicit bias of GD. This work investigates…
We provide a new computationally-efficient class of estimators for risk minimization. We show that these estimators are robust for general statistical models: in the classical Huber epsilon-contamination model and in heavy-tailed settings.…
We present a brief overview of random matrix theory (RMT) with the objectives of highlighting the computational results and applications in financial markets as complex systems. An oft-encountered problem in computational finance is the…
Reinforcement Learning (RL) applied to financial problems has been the subject of a lively area of research. The use of RL for optimal trading strategies that exploit latent information in the market is, to the best of our knowledge, not…
We study the implicit regularization effects induced by (observation) weighting of pretrained features. For weight and feature matrices of bounded operator norms that are infinitesimally free with respect to (normalized) trace functionals,…
We study the problem of evaluating the excess risk of large-scale empirical risk minimization under the square loss. Leveraging the idea of wild refitting and resampling, we assume only black-box access to the training algorithm and develop…
By using the framework of Determinantal Point Processes (DPPs), some theoretical results concerning the interplay between diversity and regularization can be obtained. In this paper we show that sampling subsets with kDPPs results in…
Online decision tree learning algorithms typically examine all features of a new data point to update model parameters. We propose a novel alternative, Reinforcement Learning- based Decision Trees (RLDT), that uses Reinforcement Learning…
We study the entanglement entropy of a random tensor network (RTN) using tools from free probability theory. Random tensor networks are simple toy models that help the understanding of the entanglement behavior of a boundary region in the…
In this work we investigate the generalization performance of random feature ridge regression (RFRR). Our main contribution is a general deterministic equivalent for the test error of RFRR. Specifically, under a certain concentration…
Data exhibiting heavy-tails in one or more dimensions is often studied using the framework of regular variation. In a multivariate setting this requires identifying specific forms of dependence in the data; this means identifying that the…
We study the learning properties of nonparametric ridge-less least squares. In particular, we consider the common case of estimators defined by scale dependent kernels, and focus on the role of the scale. These estimators interpolate the…
Multivariate statistical analysis is concerned with observations on several variables which are thought to possess some degree of inter-dependence. Driven by problems in genetics and the social sciences, it first flowered in the earlier…
In Regression Discontinuity (RD) design, self-selection leads to different distributions of covariates on two sides of the policy intervention, which essentially violates the continuity of potential outcome assumption. The standard RD…
Data subject to heavy-tailed errors are commonly encountered in various scientific fields, especially in the modern era with explosion of massive data. To address this problem, procedures based on quantile regression and Least Absolute…
High-dimensional prediction with multiple data types needs to account for potentially strong differences in predictive signal. Ridge regression is a simple model for high-dimensional data that has challenged the predictive performance of…
The field of risk-constrained reinforcement learning (RCRL) has been developed to effectively reduce the likelihood of worst-case scenarios by explicitly handling risk-measure-based constraints. However, the nonlinearity of risk measures…
We provide exact asymptotic expressions for the performance of regression by an $L-$layer deep random feature (RF) model, where the input is mapped through multiple random embedding and non-linear activation functions. For this purpose, we…
A fundamental problem in multivariate analysis is testing general linear hypotheses for regression coefficients in a multivariate linear model. This framework encompasses a wide range of well-studied tasks, including MANOVA, joint…
We introduce a discriminative regression approach to supervised classification in this paper. It estimates a representation model while accounting for discriminativeness between classes, thereby enabling accurate derivation of categorical…