Related papers: Principled Inference in Dense High-Dimensional Lin…
In many scientific disciplines structures in high-dimensional data have to be found, e.g., in stellar spectra, in genome data, or in face recognition tasks. In this work we present a novel approach to non-linear dimensionality reduction. It…
Networks are a unifying framework for modeling complex systems and network inference problems are frequently encountered in many fields. Here, I develop and apply a generative approach to network inference (RCweb) for the case when the…
Deep neural networks (DNNs) are computationally/memory-intensive and vulnerable to adversarial attacks, making them prohibitive in some real-world applications. By converting dense models into sparse ones, pruning appears to be a promising…
Convolutional neural networks (CNNs) are reported to be overparametrized. The search for optimal (minimal) and sufficient architecture is an NP-hard problem as the hyperparameter space for possible network configurations is vast. Here, we…
State-space models (SSMs) are powerful probabilistic tools for modeling time-varying systems with latent dynamics. Inference in SSMs involves the estimation of latent states and parameters. In this work, we focus on parameter inference,…
We consider inference for the mean and covariance functions of covariate adjusted functional data using Local Linear Kernel (LLK) estimators. By means of a double asymptotic, we differentiate between sparse and dense covariate adjusted…
We introduce Neural Parameter Regression (NPR), a novel framework specifically developed for learning solution operators in Partial Differential Equations (PDEs). Tailored for operator learning, this approach surpasses traditional DeepONets…
We study sparse linear regression over a network of agents, modeled as an undirected graph (with no centralized node). The estimation problem is formulated as the minimization of the sum of the local LASSO loss functions plus a quadratic…
We develop a constructive approach to estimating sparse, high-dimensional linear regression models. The approach is a computational algorithm motivated from the KKT conditions for the $\ell_0$-penalized least squares solutions. It generates…
Local polynomial regression of order one or higher often performs poorly in areas with sparse data. In contrast, local constant regression tends to be more robust in these regions, although it is generally the least accurate approach,…
Reliable and energy-efficient wireless data transmission remains a major challenge in resource-constrained wireless neural recording tasks, where data compression is generally adopted to relax the burdens on the wireless data link.…
In this work, we explore the theoretical properties of conditional deep generative models under the statistical framework of distribution regression where the response variable lies in a high-dimensional ambient space but concentrates…
Recently, tensor data (or multidimensional array) have been generated in many modern applications, such as functional magnetic resonance imaging (fMRI) in neuroscience and videos in video analysis. Many efforts are made in recent years to…
This paper provides a comprehensive estimation framework via nuclear norm plus $l_1$ norm penalization for high-dimensional approximate factor models with a sparse residual covariance. The underlying assumptions allow for non-pervasive…
Adoption of deep neural networks in fields such as economics or finance has been constrained by the lack of interpretability of model outcomes. This paper proposes a generative neural network architecture - the parameter encoder neural…
For reliability, it is important that the predictions made by machine learning methods are interpretable by human. In general, deep neural networks (DNNs) can provide accurate predictions, although it is difficult to interpret why such…
Identifying the structural priors that enable Deep Neural Networks (DNNs) to overcome the curse of dimensionality is a fundamental challenge in machine learning theory. Existing literature suggests that effective high-dimensional learning…
Deep neural networks (DNNs) have shown to provide superb performance in many real life applications, but their large computation cost and storage requirement have prevented them from being deployed to many edge and internet-of-things (IoT)…
Sparse regression on a library of candidate features has developed as the prime method to discover the partial differential equation underlying a spatio-temporal data-set. These features consist of higher order derivatives, limiting model…
High-dimensional sparse modeling with censored survival data is of great practical importance, as exemplified by modern applications in high-throughput genomic data analysis and credit risk analysis. In this article, we propose a class of…