Related papers: Limit properties of the monotone rearrangement for…
Threshold phenomena are investigated using a general approach, following Talagrand [Ann. Probab. 22 (1994) 1576--1587] and Friedgut and Kalai [Proc. Amer. Math. Soc. 12 (1999) 1017--1054]. The general upper bound for the threshold width of…
A number of generalizations of stochastic and information-theoretic randomness are known in the literature. However, they are not compatible with handling meaning in vague and dynamic contexts of rough reasoning (and therefore explainable…
We show that every algorithm for testing $n$-variate Boolean functions for monotonicity must have query complexity $\tilde{\Omega}(n^{1/4})$. All previous lower bounds for this problem were designed for non-adaptive algorithms and, as a…
We propose a strategy for computing the isotonic least-squares estimate of a monotone function in a general regression setting where the data are distributed across different servers and the observations across servers, though independent,…
Computing averages over a target probability density by statistical re-weighting of a set of samples with a different distribution is a strategy which is commonly adopted in fields as diverse as atomistic simulation and finance. Here we…
Probability estimation is essential for every statistical data compression algorithm. In practice probability estimation should be adaptive, recent observations should receive a higher weight than older observations. We present a…
Compressed sensing seeks to invert an underdetermined linear system by exploiting additional knowledge of the true solution. Over the last decade, several instances of compressed sensing have been studied for various applications, and for…
The covariate shift is a challenging problem in supervised learning that results from the discrepancy between the training and test distributions. An effective approach which recently drew a considerable attention in the research community…
Normal variance mixtures are a class of multivariate distributions that generalize the multivariate normal by randomizing (or mixing) the covariance matrix via multiplication by a non-negative random variable W. The multivariate t…
The Haraux function is an important tool in monotone operator theory and its applications. One of its salient properties for a maximally monotone operator is to be valued in $[0,+\infty]$ and to vanish only on the graph of the operator.…
In this overview article we will consider the deliberate restarting of algorithms, a meta technique, in order to improve the algorithm's performance, e.g., convergence rates or approximation guarantees. One of the major advantages is that…
Isotonic regression or monotone function estimation is a problem of estimating function values under monotonicity constraints, which appears naturally in many scientific fields. This paper proposes a new Bayesian method with global-local…
We consider the extent to which we can learn from a completely randomized experiment whether all individuals have treatment effects that are weakly of the same sign, a condition we call monotonicity. From a classical sampling perspective,…
Random Forest (Breiman, 2001) is a successful and widely used regression and classification algorithm. Part of its appeal and reason for its versatility is its (implicit) construction of a kernel-type weighting function on training data,…
In statistics and machine learning, logistic regression is a widely-used supervised learning technique primarily employed for binary classification tasks. When the number of observations greatly exceeds the number of predictor variables, we…
The aim of my thesis is to discuss, develop and apply the newest developments of this fascinating theory connected to modern harmonic analysis. In particular, we investigate some strong convergence result of partial sums of Vilenkin-Fourier…
Density estimation is a crucial component of many machine learning methods, and manifold learning in particular, where geometry is to be constructed from data alone. A significant practical limitation of the current density estimation…
Robust statistics traditionally focuses on outliers, or perturbations in total variation distance. However, a dataset could be corrupted in many other ways, such as systematic measurement errors and missing covariates. We generalize the…
We adopt the statistical framework on robustness proposed by Watson and Holmes in 2016 and then tackle the practical challenges that hinder its applicability to network models. The goal is to evaluate how the quality of an inference for a…
This paper considers the estimation of Shannon entropy for discrete distributions with countably infinite support. While minimax rates for finite-support distributions are established, infinite-support distributions present distinct…