Related papers: On the Convergence of the Mean Shift Algorithm in …
The purpose of this paper is to study the dynamical behavior of the sequence produced by a forward-backward algorithm involving two random maximal monotone operators and a sequence of decreasing step sizes. Defining a mean monotone operator…
Many machine learning methods assume that the training and test data follow the same distribution. However, in the real world, this assumption is very often violated. In particular, the phenomenon that the marginal distribution of the data…
One of the popular measures of central tendency that provides better representation and interesting insights of the data compared to the other measures like mean and median is the metric mode. If the analytical form of the density function…
Random Projection is a foundational research topic that connects a bunch of machine learning algorithms under a similar mathematical basis. It is used to reduce the dimensionality of the dataset by projecting the data points efficiently to…
The majority of machine learning methods can be regarded as the minimization of an unavailable risk function. To optimize the latter, given samples provided in a streaming fashion, we define a general stochastic Newton algorithm and its…
Density Estimation is one of the central areas of statistics whose purpose is to estimate the probability density function underlying the observed data. It serves as a building block for many tasks in statistical inference, visualization,…
In this paper, we extend the previous convergence results for the generalized alternating projection method applied to subspaces in [arXiv:1703.10547] to hold also for smooth manifolds. We show that the algorithm locally behaves similarly…
Mean Shift today, is widely used for mode detection and clustering. The technique though, is challenged in practice due to assumptions of isotropicity and homoscedasticity. We present an adaptive Mean Shift methodology that allows for full…
Debiased machine learning is a meta algorithm based on bias correction and sample splitting to calculate confidence intervals for functionals, i.e. scalar summaries, of machine learning algorithms. For example, an analyst may desire the…
The generalized density is a product of a density function and a weight function. For example, the average local brightness of an astronomical image is the probability of finding a galaxy times the mean brightness of the galaxy. We propose…
We propose in this paper a unifying scheme for several algorithms from the literature dedicated to the solving of monotone inclusion problems involving compositions with linear continuous operators in infinite dimensional Hilbert spaces. We…
Kernel mean embeddings are a popular tool that consists in representing probability measures by their infinite-dimensional mean embeddings in a reproducing kernel Hilbert space. When the kernel is characteristic, mean embeddings can be used…
Consider the following generalized hidden shift problem: given a function f on {0,...,M-1} x Z_N satisfying f(b,x)=f(b+1,x+s) for b=0,1,...,M-2, find the unknown shift s in Z_N. For M=N, this problem is an instance of the abelian hidden…
Stochastic gradient descent type methods are ubiquitous in machine learning, but they are only applicable to the optimization of differentiable functions. Proximal algorithms are more general and applicable to nonsmooth functions. We…
The main contributions of this paper are the proposition and the convergence analysis of a class of inertial projection-type algorithm for solving variational inequality problems in real Hilbert spaces where the underline operator is…
Random embeddings project high-dimensional spaces to low-dimensional ones; they are careful constructions which allow the approximate preservation of key properties, such as the pair-wise distances between points. Often in the field of…
The main difficulty that arises in the analysis of most machine learning algorithms is to handle, analytically and numerically, a large number of interacting random variables. In this Ph.D manuscript, we revisit an approach based on the…
This paper focuses on the problem of unbounded density ratio estimation -- an understudied yet critical challenge in statistical learning -- and its application to covariate shift adaptation. Much of the existing literature assumes that the…
We develop a computationally efficient and robust algorithm for generating pseudo-random samples from a broad class of smooth probability distributions in one and two dimensions. The algorithm is based on inverse transform sampling with a…
As machine learning models are increasingly deployed in dynamic environments, it becomes paramount to assess and quantify uncertainties associated with distribution shifts. A distribution shift occurs when the underlying data-generating…