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An antithetical concept, adaptive symmetry, to conservative symmetry in physics is proposed to understand the deep neural networks (DNNs). It characterizes the invariance of variance, where a biotic system explores different pathways of…
The k-Nearest Neighbors (kNN) classifier is a fundamental non-parametric machine learning algorithm. However, it is well known that it suffers from the curse of dimensionality, which is why in practice one often applies a kNN classifier on…
In this paper, we introduce the algorithms of Orthogonal Deep Neural Networks (OrthDNNs) to connect with recent interest of spectrally regularized deep learning methods. OrthDNNs are theoretically motivated by generalization analysis of…
Deep neural networks (DNNs) have demonstrated remarkable performance in many tasks but it often comes at a high computational cost and memory usage. Compression techniques, such as pruning and quantization, are applied to reduce the memory…
Neural networks are popular state-of-the-art models for many different tasks.They are often trained via back-propagation to find a value of the weights that correctly predicts the observed data. Although back-propagation has shown good…
Deep learning has been the engine powering many successes of data science. However, the deep neural network (DNN), as the basic model of deep learning, is often excessively over-parameterized, causing many difficulties in training,…
For the purpose of effective suppression of the cycle-skipping phenomenon in full waveform inversion (FWI), we developed a Deep Neural Network (DNN) approach to predict the absent low-frequency components by exploiting the implicit relation…
Deep neural networks (DNNs) demonstrate outstanding performance across most computer vision tasks. Some critical applications, such as autonomous driving or medical imaging, also require investigation into their behavior and the reasons…
This paper proposes using a method named Double Score Matching (DSM) to do mass-imputation and presents an application to make inferences with a nonprobability sample. DSM is a $k$-Nearest Neighbors algorithm that uses two balance scores…
Deep neural networks (DNNs) have been widely applied to solve real-world regression problems. However, selecting optimal network structures remains a significant challenge. This study addresses this issue by linking neuron selection in DNNs…
Weighted model counting (WMC) has emerged as a prevalent approach for probabilistic inference. In its most general form, WMC is #P-hard. Weighted DNF counting (weighted #DNF) is a special case, where approximations with probabilistic…
In linear regression we wish to estimate the optimum linear least squares predictor for a distribution over $d$-dimensional input points and real-valued responses, based on a small sample. Under standard random design analysis, where the…
Distributed state estimation is examined for a sensor network tasked with reconstructing a system's state through the use of a distributed and event-triggered observer. Each agent in the sensor network employs a deep neural network (DNN) to…
In spatial statistics, a common objective is to predict values of a spatial process at unobserved locations by exploiting spatial dependence. Kriging provides the best linear unbiased predictor using covariance functions and is often…
In the context of multivariate nonparametric regression with missing covariates, we propose Pattern Embedded Neural Networks (PENNs), which can be applied in conjunction with any existing imputation technique. In addition to a neural…
In this paper, we focus on distributed estimation and support recovery for high-dimensional linear quantile regression. Quantile regression is a popular alternative tool to the least squares regression for robustness against outliers and…
Approximate inference in probability models is a fundamental task in machine learning. Approximate inference provides powerful tools to Bayesian reasoning, decision making, and Bayesian deep learning. The main goal is to estimate the…
This paper presents a minimalist neural regression network as an aggregate of independent identical regression blocks that are trained simultaneously. Moreover, it introduces a new multiplicative parameter, shared by all the neural units of…
While many systems have been developed to train Graph Neural Networks (GNNs), efficient model inference and evaluation remain to be addressed. For instance, using the widely adopted node-wise approach, model evaluation can account for up to…
Dimensionality reduction is a fundamental task in modern data science. Several projection methods specifically tailored to take into account the non-linearity of the data via local embeddings have been proposed. Such methods are often based…