The classical binary classification problem is investigated when it is known in advance that the posterior probability function (or regression function) belongs to some class of functions. We introduce and analyze a method ...

We present a new general concentration-of-measure inequality and illustrate its power by applications in random combinatorics. The results find direct applications in some problems of learning theory.

We consider adaptive sequential lossy coding of bounded individual sequences when the performance is measured by the sequentially accumulated mean squared distortion. The encoder and the decoder are connected via a ...

Let a class $\F$ of densities be given. We draw an i.i.d.\ sample from a density $f$ which may or may not be in $\F$. After every $n$, one must make a guess whether $f \in \F$ or not. A class is almost surely testable if ...

Consider a random geometric graph defined on n vertices uniformly distributedin the d-dimensional unit torus. Two vertices are connected if their distance is less than a "visibility radius" rn. We consider Bluetooth networks ...

This thesis consists of two chapters on time series modelling. The first chapter introduces a class of vector autoregressive (VAR) models with a community structure for large panels of time series. In the model, the series ...

A uniform attachment tree is a random tree that is generated dynamically. Starting from a fixed “seed” tree, vertices are added sequentially by attaching each vertex to an existing vertex chosen uniformly at random. Upon ...

Introduction: Individuals in the midst of a mental health crisis frequently exhibit instability and face an elevated risk of recurring crises in the subsequent weeks, which underscores the importance of timely intervention ...

La toma secuencial de decisiones con incertidumbre cubre una amplia clase de problemas. Las aplicaciones reales requieren que los algoritmos sean computacionalmente eficientes y escalables. Nosotros estudiamos un rango ...

We study model selection strategies based on penalized empirical loss minimization. We point out a tight relationship between error estimation and data-based complexity penalization: any good error estimate may be ...