Related papers: Efficient Unbiased Sparsification

This paper proposes a novel distributed optimization framework that addresses time-varying optimization problems without requiring explicit derivative information of the objective functions. Traditional distributed methods often rely on…

The field of compressed sensing has shown that a sparse but otherwise arbitrary vector can be recovered exactly from a small number of randomly constructed linear projections (or samples). The question addressed in this paper is whether an…

Given an intractable target density $p$, variational inference (VI) attempts to find the best approximation $q$ from a tractable family $Q$. This is typically done by minimizing the exclusive Kullback-Leibler divergence, $\text{KL}(q||p)$.…

$k$-subset sampling is ubiquitous in machine learning, enabling regularization and interpretability through sparsity. The challenge lies in rendering $k$-subset sampling amenable to end-to-end learning. This has typically involved relaxing…

In complex visual recognition tasks it is typical to adopt multiple descriptors, that describe different aspects of the images, for obtaining an improved recognition performance. Descriptors that have diverse forms can be fused into a…

We construct a classifier which attains the rate of convergence $\log n/n$ under sparsity and margin assumptions. An approach close to the one met in approximation theory for the estimation of function is used to obtain this result. The…

For distributions $\mathbb{P}$ and $\mathbb{Q}$ with different supports or undefined densities, the divergence $\textrm{D}(\mathbb{P}||\mathbb{Q})$ may not exist. We define a Spread Divergence $\tilde{\textrm{D}}(\mathbb{P}||\mathbb{Q})$ on…

Classical learning theory suggests that the optimal generalization performance of a machine learning model should occur at an intermediate model complexity, with simpler models exhibiting high bias and more complex models exhibiting high…

Gaussian process regression is used throughout statistics and machine learning for prediction and uncertainty quantification. A Gaussian process is specified by its mean and covariance functions. Many covariance functions, including…

Variational Inference approximates an unnormalized distribution via the minimization of Kullback-Leibler (KL) divergence. Although this divergence is efficient for computation and has been widely used in applications, it suffers from some…

Semisupervised methods inevitably invoke some assumption that links the marginal distribution of the features to the regression function of the label. Most commonly, the cluster or manifold assumptions are used which imply that the…

The approximation of a discrete probability distribution $\mathbf{t}$ by an $M$-type distribution $\mathbf{p}$ is considered. The approximation error is measured by the informational divergence $\mathbb{D}(\mathbf{t}\Vert\mathbf{p})$, which…

In this work, we are concerned with the estimation of the predictive density of a Gaussian random vector where both the mean and the variance are unknown. In such a context, we prove the inadmissibility of the best equivariant predictive…

Given a full rank matrix $X$ with more columns than rows, consider the task of estimating the pseudo inverse $X^+$ based on the pseudo inverse of a sampled subset of columns (of size at least the number of rows). We show that this is…

We give an efficient algorithm for learning a binary function in a given class C of bounded VC dimension, with training data distributed according to P and test data according to Q, where P and Q may be arbitrary distributions over X. This…

Estimating linear, mean-square continuous functionals is a pivotal challenge in statistics. In high-dimensional contexts, this estimation is often performed under the assumption of exact model sparsity, meaning that only a small number of…

We define a novel, basic, unsupervised learning problem - learning the lowest density homogeneous hyperplane separator of an unknown probability distribution. This task is relevant to several problems in machine learning, such as…

In inverse problems, it is widely recognized that the incorporation of a sparsity prior yields a regularization effect on the solution. This approach is grounded on the a priori assumption that the unknown can be appropriately represented…

Kernel means are frequently used to represent probability distributions in machine learning problems. In particular, the well known kernel density estimator and the kernel mean embedding both have the form of a kernel mean. Unfortunately,…

The recent work by Dong & Yang (2023) showed for misspecified sparse linear bandits, one can obtain an $O\left(\epsilon\right)$-optimal policy using a polynomial number of samples when the sparsity is a constant, where $\epsilon$ is the…