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A widely believed explanation for the remarkable generalization capacities of overparameterized neural networks is that the optimization algorithms used for training induce an implicit bias towards benign solutions. To grasp this…
The use of sparse precision (inverse covariance) matrices has become popular because they allow for efficient algorithms for joint inference in high-dimensional models. Many applications require the computation of certain elements of the…
Gradient-based optimization is the foundation of deep learning and reinforcement learning. Even when the mechanism being optimized is unknown or not differentiable, optimization using high-variance or biased gradient estimates is still…
We study the performance of estimators of a sparse nonrandom vector based on an observation which is linearly transformed and corrupted by additive white Gaussian noise. Using the reproducing kernel Hilbert space framework, we derive a new…
Large reasoning models (LRMs) generate intermediate reasoning traces before producing final answers, yielding strong gains on multi-step and mathematical tasks. Yet aligning LRMs with human preferences, a crucial prerequisite for model…
Modern deep learning models generalize remarkably well in-distribution, despite being overparametrized and trained with little to no explicit regularization. Instead, current theory credits implicit regularization imposed by the choice of…
The soft-thinking paradigm for Large Language Model (LLM) reasoning can outperform the conventional discrete-token Chain-of-Thought (CoT) reasoning in some scenarios, underscoring its research and application value. However, while the…
We study a linear high-dimensional regression model in a semi-supervised setting, where for many observations only the vector of covariates $X$ is given with no response $Y$. We do not make any sparsity assumptions on the vector of…
Variational inference in Bayesian deep learning often involves computing the gradient of an expectation that lacks a closed-form solution. In these cases, pathwise and score-function gradient estimators are the most common approaches. The…
Inferring the eventual goal of a mobile agent from noisy observations of its trajectory is a fundamental estimation problem. We initiate the study of such intent inference using a variant of a Rao-Blackwellized Particle Filter (RBPF),…
Training deep generative models like Variational Autoencoders (VAEs) requires propagating gradients through stochastic latent variables, which introduces estimation variance that can slow convergence and degrade performance. In this paper,…
While the traditional formulation of machine learning tasks is in terms of performance on average, in practice we are often interested in how well a trained model performs on rare or difficult data points at test time. To achieve more…
The recent boom in the literature on entropy-regularized reinforcement learning (RL) approaches reveals that Kullback-Leibler (KL) regularization brings advantages to RL algorithms by canceling out errors under mild assumptions. However,…
This article presents differential equations and solution methods for the functions of the form $Q(x) = F^{-1}(G(x))$, where $F$ and $G$ are cumulative distribution functions. Such functions allow the direct recycling of Monte Carlo samples…
We show that for any concave utility, the expected utility of an e-variable can only increase after conditioning on a sufficient statistic. The simplest form of the result has an extremely straightforward proof, which follows from a single…
There exist several methods developed for the canonical change point problem of detecting multiple mean shifts, which search for changes over sections of the data at multiple scales. In such methods, estimation of the noise level is often…
The recently proposed Unbiased Online Recurrent Optimization algorithm (UORO, arXiv:1702.05043) uses an unbiased approximation of RTRL to achieve fully online gradient-based learning in RNNs. In this work we analyze the variance of the…
Sharpness-aware minimization (SAM) has well documented merits in enhancing generalization of deep neural networks, even without sizable data augmentation. Embracing the geometry of the loss function, where neighborhoods of 'flat minima'…
The objective of active level set estimation for a black-box function is to precisely identify regions where the function values exceed or fall below a specified threshold by iteratively performing function evaluations to gather more…
The method of "random Fourier features (RFF)" has become a popular tool for approximating the "radial basis function (RBF)" kernel. The variance of RFF is actually large. Interestingly, the variance can be substantially reduced by a simple…