相关论文: Geometric Median (GM) Matching for Robust Data Pru…

Subset selection, which aims to select a subset from a ground set to maximize some objective function, arises in various applications such as influence maximization and sensor placement. In real-world scenarios, however, one often needs to…

We consider high dimensional sparse regression, and develop strategies able to deal with arbitrary -- possibly, severe or coordinated -- errors in the covariance matrix $X$. These may come from corrupted data, persistent experimental…

Group Relative Policy Optimization (GRPO) has significantly enhanced the reasoning capability of large language models by optimizing the arithmetic mean of token-level rewards. Unfortunately, GRPO is observed to suffer from unstable policy…

We present an algorithm to compute the geometric median of shapes which is based on the extension of median to high dimensions. The median finding problem is formulated as an optimization over distances and it is solved directly using the…

This paper addresses the problem of neighborhood selection for Gaussian graphical models. We present two heuristic algorithms: a forward-backward greedy algorithm for general Gaussian graphical models based on mutual information test, and a…

Generalized linear mixed models (GLMMs) are a widely used tool in statistical analysis. The main bottleneck of many computational approaches lies in the inversion of the high dimensional precision matrices associated with the random…

An effective technique for solving optimization problems over massive data sets is to partition the data into smaller pieces, solve the problem on each piece and compute a representative solution from it, and finally obtain a solution…

There are several applications of stochastic optimization where one can benefit from a robust estimate of the gradient. For example, domains such as distributed learning with corrupted nodes, the presence of large outliers in the training…

In this paper, we consider a subset selection problem in a spatial field where we seek to find a set of k locations whose observations provide the best estimate of the field value at a finite set of prediction locations. The measurements…

Learning Gaussian Mixture Models (GMMs) is a fundamental problem in machine learning, with the Expectation-Maximization (EM) algorithm and its popular variant gradient EM being arguably the most widely used algorithms in practice. In the…

Gaussian processes (GP) for machine learning have been studied systematically over the past two decades and they are by now widely used in a number of diverse applications. However, GP kernel design and the associated hyper-parameter…

In learning theory, a standard assumption is that the data is generated from a finite mixture model. But what happens when the number of components is not known in advance? The problem of estimating the number of components, also called…

As a promising step, the performance of data analysis and feature learning are able to be improved if certain pattern matching mechanism is available. One of the feasible solutions can refer to the importance estimation of instances, and…

In this paper, we propose a novel Heterogeneous Gaussian Mechanism (HGM) to preserve differential privacy in deep neural networks, with provable robustness against adversarial examples. We first relax the constraint of the privacy budget in…

We study the fundamental problem of selecting optimal features for model construction. This problem is computationally challenging on large datasets, even with the use of greedy algorithm variants. To address this challenge, we extend the…

Greedy algorithms for minimizing L0-norm of sparse decomposition have profound application impact on many signal processing problems. In the sparse coding setup, given the observations $\mathrm{y}$ and the redundant dictionary…

Ensuring high-quality data is paramount for maximizing the performance of machine learning models and business intelligence systems. However, challenges in data quality, including noise in data capture, missing records, limited data…

Gradient Boosting Machine (GBM) introduced by Friedman is a powerful supervised learning algorithm that is very widely used in practice---it routinely features as a leading algorithm in machine learning competitions such as Kaggle and the…

Kernel based methods provide a way to reconstruct potentially high-dimensional functions from meshfree samples, i.e., sampling points and corresponding target values. A crucial ingredient for this to be successful is the distribution of the…

Cooperative Greedy Pursuit Strategies are considered for approximating a signal partition subjected to a global constraint on sparsity. The approach aims at producing a high quality sparse approximation of the whole signal, using highly…