相关论文: Structured Prediction with Abstention via the Lov\…

Empirical risk minimization frequently employs convex surrogates to underlying discrete loss functions in order to achieve computational tractability during optimization. However, classical convex surrogates can only tightly bound modular…

Classification is the most important process in data analysis. However, due to the inherent non-convex and non-smooth structure of the zero-one loss function of the classification model, various convex surrogate loss functions such as hinge…

A successful approach to structured learning is to write the learning objective as a joint function of linear parameters and inference messages, and iterate between updates to each. This paper observes that if the inference problem is…

We consider selection of random predictors for high-dimensional regression problem with binary response for a general loss function. Important special case is when the binary model is semiparametric and the response function is misspecified…

The earth system is exceedingly complex and often chaotic in nature, making prediction incredibly challenging: we cannot expect to make perfect predictions all of the time. Instead, we look for specific states of the system that lead to…

We consider the problem of binary classification with abstention in the relatively less studied \emph{bounded-rate} setting. We begin by obtaining a characterization of the Bayes optimal classifier for an arbitrary input-label distribution…

In modern classification tasks, the number of labels is getting larger and larger, as is the size of the datasets encountered in practice. As the number of classes increases, class ambiguity and class imbalance become more and more…

The paper is devoted to a special Mirror Descent algorithm for problems of convex minimization with functional constraints. The objective function may not satisfy the Lipschitz condition, but it must necessarily have the Lipshitz-continuous…

We develop new approaches in multi-class settings for constructing proper scoring rules and hinge-like losses and establishing corresponding regret bounds with respect to the zero-one or cost-weighted classification loss. Our construction…

We define "decision swap regret" which generalizes both prediction for downstream swap regret and omniprediction, and give algorithms for obtaining it for arbitrary multi-dimensional Lipschitz loss functions in online adversarial settings.…

Support vector machines (SVMs) naturally embody sparseness due to their use of hinge loss functions. However, SVMs can not directly estimate conditional class probabilities. In this paper we propose and study a family of coherence…

The Lovasz Local Lemma [EL75] is a powerful tool to non-constructively prove the existence of combinatorial objects meeting a prescribed collection of criteria. In his breakthrough paper [Bec91], Beck demonstrated that a constructive…

We propose a novel hybrid loss for multiclass and structured prediction problems that is a convex combination of log loss for Conditional Random Fields (CRFs) and a multiclass hinge loss for Support Vector Machines (SVMs). We provide a…

We consider a general conic mixed-binary set where each homogeneous conic constraint $j$ involves an affine function of independent continuous variables and an epigraph variable associated with a nonnegative function, $f_j$, of common…

In this paper we consider skew bisubmodular functions as introduced in [9]. We construct a convex extension of a skew bisubmodular function which we call Lov\'asz extension in correspondence to the submodular case. We use this extension to…

In this paper, we study classes of discrete convex functions: submodular functions on modular semilattices and L-convex functions on oriented modular graphs. They were introduced by the author in complexity classification of minimum…

In model selection problems for machine learning, the desire for a well-performing model with meaningful structure is typically expressed through a regularized optimization problem. In many scenarios, however, the meaningful structure is…

In this work, we consider a binary classification problem and cast it into a binary hypothesis testing framework, where the observations can be perturbed by an adversary. To improve the adversarial robustness of a classifier, we include an…

Performative prediction is a framework for learning models that influence the data they intend to predict. We focus on finding classifiers that are performatively stable, i.e. optimal for the data distribution they induce. Standard…

This thesis studies two problems in modern statistics. First, we study selective inference, or inference for hypothesis that are chosen after looking at the data. The motiving application is inference for regression coefficients selected by…