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Swarms evolving from collective behaviors among multiple individuals are commonly seen in nature, which enables biological systems to exhibit more efficient and robust collaboration. Creating similar swarm intelligence in engineered robots…
Stochastic approximation algorithm is a useful technique which has been exploited successfully in probability theory and statistics for a long time. The step sizes used in stochastic approximation are generally taken to be deterministic and…
Symmetry, a central concept in understanding the laws of nature, has been used for centuries in physics, mathematics, and chemistry, to help make mathematical models tractable. Yet, despite its power, symmetry has not been used extensively…
For any finite point set in $D$-dimensional space equipped with the 1-norm, we present random linear embeddings to $k$-dimensional space, with a new metric, having the following properties. For any pair of points from the point set that are…
Reconstructing the 3D model of a physical object typically requires us to align the depth scans obtained from different camera poses into the same coordinate system. Solutions to this global alignment problem usually proceed in two steps.…
In machine learning models, the estimation of errors is often complex due to distribution bias, particularly in spatial data such as those found in environmental studies. We introduce an approach based on the ideas of importance sampling to…
We consider centralized and distributed mirror descent algorithms over a finite-dimensional Hilbert space, and prove that the problem variables converge to an optimizer of a possibly nonsmooth function when the step sizes are square…
Consensus algorithms are popular distributed algorithms for computing aggregate quantities, such as averages, in ad-hoc wireless networks. However, existing algorithms mostly address the case where the measurements lie in a Euclidean space.…
Approximating a probability distribution using a set of particles is a fundamental problem in machine learning and statistics, with applications including clustering and quantization. Formally, we seek a weighted mixture of Dirac measures…
In this paper we address the convergence of stochastic approximation when the functions to be minimized are not convex and nonsmooth. We show that the "mean-limit" approach to the convergence which leads, for smooth problems, to the ODE…
We study the machine learning task for models with operators mapping between the Wasserstein space of probability measures and a space of functions, like e.g. in mean-field games/control problems. Two classes of neural networks, based on…
We provide quantitative information in the form of a rate of metastability in the sense of T. Tao and (under a metric regularity assumption) a rate of convergence for an algorithm approximating zeros of differences of maximally monotone…
Many randomized approximation algorithms operate by giving a procedure for simulating a random variable $X$ which has mean $\mu$ equal to the target answer, and a relative standard deviation bounded above by a known constant $c$. Examples…
We present a generalization of the bilateral filter that can be applied to feature-preserving smoothing of signals on images, meshes, and other domains within a single unified framework. Our discretization is competitive with…
We study the block-coordinate forward-backward algorithm in which the blocks are updated in a random and possibly parallel manner, according to arbitrary probabilities. The algorithm allows different stepsizes along the block-coordinates to…
In this paper, the Mean value iterative process is modified with the Mann iterative process for mean nonexpansive mapping in a hyperbolic metric space that satisfy the symmetry criteria and in uniformly convex hyperbolic spaces to validate…
Random Reshuffling (RR) is an algorithm for minimizing finite-sum functions that utilizes iterative gradient descent steps in conjunction with data reshuffling. Often contrasted with its sibling Stochastic Gradient Descent (SGD), RR is…
A default assumption in many machine learning scenarios is that the training and test samples are drawn from the same probability distribution. However, such an assumption is often violated in the real world due to non-stationarity of the…
Covariate shifts are a common problem in predictive modeling on real-world problems. This paper proposes addressing the covariate shift problem by minimizing Maximum Mean Discrepancy (MMD) statistics between the training and test sets in…
Deep metric learning algorithms have been utilized to learn discriminative and generalizable models which are effective for classifying unseen classes. In this paper, a novel noise tolerant deep metric learning algorithm is proposed. The…