Related papers: Random projections: data perturbation for classifi…
Sketching, a dimensionality reduction technique, has received much attention in the statistics community. In this paper, we study sketching in the context of Newton's method for solving finite-sum optimization problems in which the number…
The immense amount of daily generated and communicated data presents unique challenges in their processing. Clustering, the grouping of data without the presence of ground-truth labels, is an important tool for drawing inferences from data.…
In this work, we study distributed sketching methods for large scale regression problems. We leverage multiple randomized sketches for reducing the problem dimensions as well as preserving privacy and improving straggler resilience in…
Subsampled Randomized Hadamard Transform (SRHT), a popular random projection method that can efficiently project a $d$-dimensional data into $r$-dimensional space ($r \ll d$) in $O(dlog(d))$ time, has been widely used to address the…
Besides serving as prediction models, classification trees are useful for finding important predictor variables and identifying interesting subgroups in the data. These functions can be compromised by weak split selection algorithms that…
Modern technologies are generating ever-increasing amounts of data. Making use of these data requires methods that are both statistically sound and computationally efficient. Typically, the statistical and computational aspects are treated…
Classification is an important statistical learning tool. In real application, besides high prediction accuracy, it is often desirable to estimate class conditional probabilities for new observations. For traditional problems where the…
A method is introduced for studying large deviations in the context of statistical physics of disordered systems. The approach, based on an extension of the cavity method to atypical realizations of the quenched disorder, allows us to…
The paper addresses the $k$-tangle enumeration problem. We introduce a notion of cascade diagram for $k$-tangle projections. An effective enumeration algorithm for projections is proposed based on cascade representation. Tangles projections…
Embeddings provide compact representations of signals in order to perform efficient inference in a wide variety of tasks. In particular, random projections are common tools to construct Euclidean distance-preserving embeddings, while…
In contrast to classical reinforcement learning (RL), distributional RL algorithms aim to learn the distribution of returns rather than their expected value. Since the nature of the return distribution is generally unknown a priori or…
Ranking problems, also known as preference learning problems, define a widely spread class of statistical learning problems with many applications, including fraud detection, document ranking, medicine, credit risk screening, image ranking…
In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known.…
For many applications in signal processing and machine learning, we are tasked with minimizing a large sum of convex functions subject to a large number of convex constraints. In this paper, we devise a new random projection method (RPM) to…
We introduce a very general method for sparse and large-scale variable selection. The large-scale regression settings is such that both the number of parameters and the number of samples are extremely large. The proposed method is based on…
A projective rectangle is like a projective plane that has different lengths in two directions. We develop the basic theory of projective rectangles including incidence properties, projective subplanes, configuration counts, a partial…
We develop hybrid projection methods for computing solutions to large-scale inverse problems, where the solution represents a sum of different stochastic components. Such scenarios arise in many imaging applications (e.g., anomaly detection…
Modern large-scale statistical models require to estimate thousands to millions of parameters. This is often accomplished by iterative algorithms such as gradient descent, projected gradient descent or their accelerated versions. What are…
The last decade has seen a revolution in the theory and application of machine learning and pattern recognition. Through these advancements, variable ranking has emerged as an active and growing research area and it is now beginning to be…
This paper presents two novel algorithms for approximately projecting symmetric matrices onto the Positive Semidefinite (PSD) cone using Randomized Numerical Linear Algebra (RNLA). Classical PSD projection methods rely on full-rank…