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Incorporating sparsity priors in learning tasks can give rise to simple, and interpretable models for complex high dimensional data. Sparse models have found widespread use in structure discovery, recovering data from corruptions, and a…
To accelerate kernel methods, we propose a near input sparsity time algorithm for sampling the high-dimensional feature space implicitly defined by a kernel transformation. Our main contribution is an importance sampling method for…
We review connections between coding-theoretic objects and sparse learning problems. In particular, we show how seemingly different combinatorial objects such as error-correcting codes, combinatorial designs, spherical codes, compressed…
Sparse PCA is one of the most well-studied problems in high-dimensional statistics. In this problem, we are given samples from a distribution with covariance $\Sigma$, whose top eigenvector $v \in R^d$ is $s$-sparse. Existing sparse PCA…
Entanglement entropy for a spatial partition of a quantum system is studied in theories which admit a dual description in terms of the anti-de Sitter (AdS) gravity one dimension higher. A general proof of the holographic formula which…
Training and inference on edge devices often requires an efficient setup due to computational limitations. While pre-computing data representations and caching them on a server can mitigate extensive edge device computation, this leads to…
Fault intensity diagnosis (FID) plays a pivotal role in monitoring and maintaining mechanical devices within complex industrial systems. As current FID methods are based on chain of thought without considering dependencies among target…
Multi-label learning is concerned with the classification of data with multiple class labels. This is in contrast to the traditional classification problem where every data instance has a single label. Due to the exponential size of output…
Learning compact binary codes for image retrieval problem using deep neural networks has recently attracted increasing attention. However, training deep hashing networks is challenging due to the binary constraints on the hash codes. In…
We study dynamic algorithms robust to adaptive input generated from sources with bounded capabilities, such as sparsity or limited interaction. For example, we consider robust linear algebraic algorithms when the updates to the input are…
Quadratic regression involves modeling the response as a (generalized) linear function of not only the features $x^{j_1}$ but also of quadratic terms $x^{j_1}x^{j_2}$. The inclusion of such higher-order "interaction terms" in regression…
We consider probabilistic topic models and more recent word embedding techniques from a perspective of learning hidden semantic representations. Inspired by a striking similarity of the two approaches, we merge them and learn probabilistic…
How does word frequency in pre-training data affect the behavior of similarity metrics in contextualized BERT embeddings? Are there systematic ways in which some word relationships are exaggerated or understated? In this work, we explore…
Problem definition: A key challenge in supervised learning is data scarcity, which can cause prediction models to overfit to the training data and perform poorly out of sample. A contemporary approach to combat overfitting is offered by…
Word embeddings are trained to predict word cooccurrence statistics, which leads them to possess different lexical properties (syntactic, semantic, etc.) depending on the notion of context defined at training time. These properties manifest…
In this article a unified approach to iterative soft-thresholding algorithms for the solution of linear operator equations in infinite dimensional Hilbert spaces is presented. We formulate the algorithm in the framework of generalized…
Variational Bayesian inference is an important machine-learning tool that finds application from statistics to robotics. The goal is to find an approximate probability density function (PDF) from a chosen family that is in some sense…
Feature selection is a dimensionality reduction technique that selects a subset of representative features from high dimensional data by eliminating irrelevant and redundant features. Recently, feature selection combined with sparse…
Polynomial optimization problems are infinite-dimensional, nonconvex, NP-hard, and are often handled in practice with the moment-sums of squares hierarchy of semidefinite programming bounds. We consider problems where the objective function…
Query evaluation over probabilistic databases is known to be intractable in many cases, even in data complexity, i.e., when the query is fixed. Although some restrictions of the queries [19] and instances [4] have been proposed to lower the…