Related papers: Frequency Analysis with Multiple Kernels and Compl…

This research paper presents a comprehensive analysis of integrating advanced language models with search and retrieval systems in the fields of information retrieval and natural language processing. The objective is to evaluate and compare…

Optimal frequency identification in astronomical datasets is crucial for variable star studies, exoplanet detection, and asteroseismology. Traditional period-finding methods often rely on specific parametric assumptions, employ binning…

When performing an analysis on a collection of molecular sequences, it can be convenient to reduce the number of sequences under consideration while maintaining some characteristic of a larger collection of sequences. For example, one may…

The Expectation Maximization (EM) algorithm is the default algorithm for inference in latent variable models. As in any other field of machine learning, applications of latent variable models to very large datasets make the use of advanced…

A recurrent theme in functional analysis is the interplay between the theory of positive definite functions, and their reproducing kernels, on the one hand, and Gaussian stochastic processes, on the other. This central theme is motivated by…

Expressiveness and generalization of deep models was recently addressed via the connection between neural networks (NNs) and kernel learning, where first-order dynamics of NN during a gradient-descent (GD) optimization were related to…

Greedy algorithms are popular in compressive sensing for their high computational efficiency. But the performance of current greedy algorithms can be degenerated seriously by noise (both multiplicative noise and additive noise). A robust…

Let \phi(G) be the minimum conductance of an undirected graph G, and let 0=\lambda_1 <= \lambda_2 <=... <= \lambda_n <= 2 be the eigenvalues of the normalized Laplacian matrix of G. We prove that for any graph G and any k >= 2, \phi(G) =…

Probabilistic machine learning models are distinguished by their ability to integrate prior knowledge of noise statistics, smoothness parameters, and training data uncertainty. A common approach involves modeling data with Gaussian…

Compressive sampling (CoSa) has provided many methods for signal recovery of signals compressible with respect to an orthonormal basis. However, modern applications have sparked the emergence of approaches for signals not sparse in an…

We propose a principled method for kernel learning, which relies on a Fourier-analytic characterization of translation-invariant or rotation-invariant kernels. Our method produces a sequence of feature maps, iteratively refining the SVM…

First-order optimization (FOO) algorithms are pivotal in numerous computational domains such as machine learning and signal denoising. However, their application to complex tasks like neural network training often entails significant…

This is a parallelized algorithm performing a decomposition of a noisy time series into a number of sinusoidal components. The algorithm analyses all suspicious periodicities that can be revealed, including the ones that look like an alias…

In a recent paper, Hou and Shi introduced a new adaptive data analysis method to analyze nonlinear and non-stationary data. The main idea is to look for the sparsest representation of multiscale data within the largest possible dictionary…

Optimal sampling of non band-limited functions is an issue of great importance that has attracted considerable attention. We propose to tackle this problem through the use of a frequency warping: First, by a nonlinear shrinking of…

In big data image/video analytics, we encounter the problem of learning an overcomplete dictionary for sparse representation from a large training dataset, which can not be processed at once because of storage and computational constraints.…

Dictionary learning is a cutting-edge area in imaging processing, that has recently led to state-of-the-art results in many signal processing tasks. The idea is to conduct a linear decomposition of a signal using a few atoms of a learned…

Crowd counting has gained significant popularity due to its practical applications. However, mainstream counting methods ignore precise individual localization and suffer from annotation noise because of counting from estimating density…

In order to fully utilize "big data", it is often required to use "big models". Such models tend to grow with the complexity and size of the training data, and do not make strong parametric assumptions upfront on the nature of the…

We propose an efficient algorithm for solving orthogonal canonical correlation analysis (OCCA) in the form of trace-fractional structure and orthogonal linear projections. Even though orthogonality has been widely used and proved to be a…