Related papers: The Structured Abstain Problem and the Lov\'asz Hi…
We study consistency properties of surrogate loss functions for general multiclass learning problems, defined by a general multiclass loss matrix. We extend the notion of classification calibration, which has been studied for binary and…
The Lopsided Lovasz Local Lemma (LLLL) is a cornerstone probabilistic tool for showing that it is possible to avoid a collection of "bad" events as long as their probabilities and interdependencies are sufficiently small. The strongest…
Learning with abstention is a key scenario where the learner can abstain from making a prediction at some cost. In this paper, we analyze the score-based formulation of learning with abstention in the multi-class classification setting. We…
We study the key framework of learning with abstention in the multi-class classification setting. In this setting, the learner can choose to abstain from making a prediction with some pre-defined cost. We present a series of new theoretical…
Sparsity-inducing penalties are useful tools to design multiclass support vector machines (SVMs). In this paper, we propose a convex optimization approach for efficiently and exactly solving the multiclass SVM learning problem involving a…
The Lovasz Local Lemma [EL75] is a powerful tool to prove the existence of combinatorial objects meeting a prescribed collection of criteria. The technique can directly be applied to the satisfiability problem, yielding that a k-CNF formula…
Large language models (LLMs) have achieved remarkable performance but face critical challenges: hallucinations and high inference costs. Leveraging multiple experts offers a solution: deferring uncertain inputs to more capable experts…
The choice of loss function in classification involves a fundamental trade-off: smooth losses (like Cross-Entropy) enable fast optimization rates but yield slow square-root consistency bounds, while piecewise-linear losses (like Hinge)…
Given an undirected graph, the Densest-k-Subgraph problem (DkS) seeks to find a subset of k vertices such that the sum of the edge weights in the corresponding subgraph is maximized. The problem is known to be NP-hard, and is also very…
A key problem in statistics and machine learning is the determination of network structure from data. We consider the case where the structure of the graph to be reconstructed is known to be scale-free. We show that in such cases it is…
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…
Ranked decision systems -- recommenders, ad auctions, clinical triage queues -- must decide when to intervene in ranked outputs and when to abstain. We study when confidence-based abstention monotonically improves decision quality, and when…
We consider a stochastic version of the proximal point algorithm for optimization problems posed on a Hilbert space. A typical application of this is supervised learning. While the method is not new, it has not been extensively analyzed in…
Graphical models for structured domains are powerful tools, but the computational complexities of combinatorial prediction spaces can force restrictions on models, or require approximate inference in order to be tractable. Instead of…
We propose a robust adversarial prediction framework for general multiclass classification. Our method seeks predictive distributions that robustly optimize non-convex and non-continuous multiclass loss metrics against the worst-case…
Recent research has introduced a key notion of $H$-consistency bounds for surrogate losses. These bounds offer finite-sample guarantees, quantifying the relationship between the zero-one estimation error (or other target loss) and the…
We study the problem of classification with a reject option for a fixed predictor, applicable in natural language processing. We introduce a new problem formulation for this scenario, and an algorithm minimizing a new surrogate loss…
This work theoretically studies the problem of estimating a structured high-dimensional signal $x_0 \in \mathbb{R}^n$ from noisy $1$-bit Gaussian measurements. Our recovery approach is based on a simple convex program which uses the hinge…
We explore the problem of binary classification in machine learning, with a twist - the classifier is allowed to abstain on any datum, professing ignorance about the true class label without committing to any prediction. This is directly…
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…