Related papers: Low-rank data modeling via the Minimum Description…
A fundamental problem associated with the task of network reconstruction from dynamical or behavioral data consists in determining the most appropriate model complexity in a manner that prevents overfitting, and produces an inferred network…
The "Curse of dimensionality" is prevalent across various data patterns, which increases the risk of model overfitting and leads to a decline in model classification performance. However, few studies have focused on this issue in Partial…
Dynamic Mode Decomposition (DMD) has emerged as a powerful tool for analyzing the dynamics of non-linear systems from experimental datasets. Recently, several attempts have extended DMD to the context of low-rank approximations. This…
The task of reconstructing a matrix given a sample of observedentries is known as the matrix completion problem. It arises ina wide range of problems, including recommender systems, collaborativefiltering, dimensionality reduction, image…
Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…
Despite many modern applications of Deep Neural Networks (DNNs), the large number of parameters in the hidden layers makes them unattractive for deployment on devices with storage capacity constraints. In this paper we propose a Data-Driven…
Deep neural networks trained through end-to-end learning have achieved remarkable success across various domains in the past decade. However, the end-to-end learning strategy, originally designed to minimize predictive loss in a black-box…
We study modeling and identification of processes with a spectral density matrix of low rank. Equivalently, we consider processes having an innovation of reduced dimension for which Prediction Error Methods (PEM) algorithms are not directly…
A key issue in statistics and machine learning is to automatically select the "right" model complexity, e.g., the number of neighbors to be averaged over in k nearest neighbor (kNN) regression or the polynomial degree in regression with…
This paper introduces a new notion of dimensionality of probabilistic models from an information-theoretic view point. We call it the "descriptive dimension"(Ddim). We show that Ddim coincides with the number of independent parameters for…
Graph pooling compresses graphs and summarises their topological properties and features in a vectorial representation. It is an essential part of deep graph representation learning and is indispensable in graph-level tasks like…
We investigate the problem of best policy identification in discounted linear Markov Decision Processes in the fixed confidence setting under a generative model. We first derive an instance-specific lower bound on the expected number of…
We consider the problem of recovering low-rank matrices from random rank-one measurements, which spans numerous applications including covariance sketching, phase retrieval, quantum state tomography, and learning shallow polynomial neural…
Reduced-rank linear discriminant analysis (RRLDA) is a foundational method of dimension reduction for classification that has been useful in a wide range of applications. The goal is to identify an optimal subspace to project the…
High-quality training data is critical to the performance of large language models (LLMs). Recent work has explored using LLMs to rate and select data based on a small set of human-designed criteria (rules), but these approaches often rely…
Robust matrix completion (RMC) is a widely used machine learning tool that simultaneously tackles two critical issues in low-rank data analysis: missing data entries and extreme outliers. This paper proposes a novel scalable and learnable…
We consider offline Reinforcement Learning (RL), where the agent does not interact with the environment and must rely on offline data collected using a behavior policy. Previous works provide policy evaluation guarantees when the target…
Fast and effective unsupervised anomaly detection algorithms have been proposed for categorical data based on the minimum description length (MDL) principle. However, they can be ineffective when detecting anomalies in heterogeneous…
This paper describes a new algorithm for computing Nonnegative Low Rank Matrix (NLRM) approximation for nonnegative matrices. Our approach is completely different from classical nonnegative matrix factorization (NMF) which has been studied…
This paper is concerned with the problem of low rank plus sparse matrix decomposition for big data. Conventional algorithms for matrix decomposition use the entire data to extract the low-rank and sparse components, and are based on…