Related papers: Classification with Minimax Fast Rates for Classes…

We formulate the sparse classification problem of $n$ samples with $p$ features as a binary convex optimization problem and propose a cutting-plane algorithm to solve it exactly. For sparse logistic regression and sparse SVM, our algorithm…

We consider model selection and estimation for partial spline models and propose a new regularization method in the context of smoothing splines. The regularization method has a simple yet elegant form, consisting of roughness penalty on…

This paper addresses identification of sparse linear and noise-driven continuous-time state-space systems, i.e., the right-hand sides in the dynamical equations depend only on a subset of the states. The key assumption in this study, is…

Models with dimension more than the available sample size are now commonly used in various applications. A sensible inference is possible using a lower-dimensional structure. In regression problems with a large number of predictors, the…

We take a Bayesian perspective to illustrate a connection between training speed and the marginal likelihood in linear models. This provides two major insights: first, that a measure of a model's training speed can be used to estimate its…

Within a Bayesian decision theoretic framework we investigate some asymptotic optimality properties of a large class of multiple testing rules. A parametric setup is considered, in which observations come from a normal scale mixture model…

This dissertation shows that careful injection of noise into sample data can substantially speed up Expectation-Maximization algorithms. Expectation-Maximization algorithms are a class of iterative algorithms for extracting maximum…

The vast majority of statistical theory on binary classification characterizes performance in terms of accuracy. However, accuracy is known in many cases to poorly reflect the practical consequences of classification error, most famously in…

We consider learning methods based on the regularization of a convex empirical risk by a squared Hilbertian norm, a setting that includes linear predictors and non-linear predictors through positive-definite kernels. In order to go beyond…

This study is about inducing classifiers using data that is imbalanced, with a minority class being under-represented in relation to the majority classes. The first section of this research focuses on the main characteristics of data that…

Variational sparsity regularization based on $\ell^1$-norms and other nonlinear functionals has gained enormous attention recently, both with respect to its applications and its mathematical analysis. A focus in regularization theory has…

We show that a simple modification of the 1-nearest neighbor classifier yields a strongly Bayes consistent learner. Prior to this work, the only strongly Bayes consistent proximity-based method was the k-nearest neighbor classifier, for k…

Suppose $X_1,\dots, X_n$ is a random sample from a bounded and decreasing density $f_0$ on $[0,\infty)$. We are interested in estimating such $f_0$, with special interest in $f_0(0)$. This problem is encountered in various statistical…

This paper deals with the following question: Suppose that there exist an integer or a non-negative integer solution $x$ to a system $Ax = b$, where the number of non-zero components of $x$ is $n$. The target is, for a given natural number…

Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency,…

In the Naive Bayes classification model the class conditional densities are estimated as the products of their marginal densities along the cardinal basis directions. We study the problem of obtaining an alternative basis for this…

In this article, we study rates of convergence of the generalization error of multi-class margin classifiers. In particular, we develop an upper bound theory quantifying the generalization error of various large margin classifiers. The…

In this work, we study a new approach to optimizing the margin distribution realized by binary classifiers. The classical approach to this problem is simply maximization of the expected margin, while more recent proposals consider…

We derive a family of loss functions to train models in the presence of sampling bias. Examples are when the prevalence of a pathology differs from its sampling rate in the training dataset, or when a machine learning practioner rebalances…

In the synthesis model signals are represented as a sparse combinations of atoms from a dictionary. Dictionary learning describes the acquisition process of the underlying dictionary for a given set of training samples. While ideally this…