Abstract-Real-world tasks in computer vision often touch upon open set recognition: multi-class recognition with incomplete knowledge of the world and many unknown inputs. Recent work on this problem has proposed a model incorporating an open space risk term to account for the space beyond the reasonable support of known classes. This article extends the general idea of open space risk limiting classification to accommodate non-linear classifiers in a multi-class setting. We introduce a new open set recognition model called Compact Abating Probability (CAP), where the probability of class membership decreases in value (abates) as points move from known data toward open space. We show that CAP models improve open set recognition for multiple algorithms. Leveraging the CAP formulation, we go on to describe the novel Weibull-calibrated SVM (W-SVM) algorithm, which combines the useful properties of statistical extreme value theory for score calibration with one-class and binary support vector machines. Our experiments show that the W-SVM is significantly better for open set object detection and OCR problems when compared to the state-of-the-art for the same tasks.
Abstract-It is often desirable to be able to recognize when inputs to a recognition function learned in a supervised manner correspond to classes unseen at training time. With this ability, new class labels could be assigned to these inputs by a human operator, allowing them to be incorporated into the recognition function -ideally under an efficient incremental update mechanism. While good algorithms that assume inputs from a fixed set of classes exist, e.g., artificial neural networks and kernel machines, it is not immediately obvious how to extend them to perform incremental learning in the presence of unknown query classes. Existing algorithms take little to no distributional information into account when learning recognition functions and lack a strong theoretical foundation. We address this gap by formulating a novel, theoretically sound classifier -the Extreme Value Machine (EVM). The EVM has a wellgrounded interpretation derived from statistical Extreme Value Theory (EVT), and is the first classifier to be able to perform nonlinear kernel-free variable bandwidth incremental learning. Compared to other classifiers in the same deep network derived feature space, the EVM is accurate and efficient on an established benchmark partition of the ImageNet dataset.
Abstract. The perceived success of recent visual recognition approaches has largely been derived from their performance on classification tasks, where all possible classes are known at training time. But what about open set problems, where unknown classes appear at test time? Intuitively, if we could accurately model just the positive data for any known class without overfitting, we could reject the large set of unknown classes even under an assumption of incomplete class knowledge. In this paper, we formulate the problem as one of modeling positive training data at the decision boundary, where we can invoke the statistical extreme value theory. A new algorithm called the PI -SVM is introduced for estimating the unnormalized posterior probability of class inclusion.
In this paper we introduce the transductive linear bandit problem: given a set of measurement vectors X ⊂ R d , a set of items Z ⊂ R d , a fixed confidence δ, and an unknown vector θ * ∈ R d , the goal is to infer argmax z∈Z z θ * with probability 1 − δ by making as few sequentially chosen noisy measurements of the form x θ * as possible. When X = Z, this setting generalizes linear bandits, and when X is the standard basis vectors and Z ⊂ {0, 1} d , combinatorial bandits. Such a transductive setting naturally arises when the set of measurement vectors is limited due to factors such as availability or cost. As an example, in drug discovery the compounds and dosages X a practitioner may be willing to evaluate in the lab in vitro due to cost or safety reasons may differ vastly from those compounds and dosages Z that can be safely administered to patients in vivo. Alternatively, in recommender systems for books, the set of books X a user is queried about may be restricted to well known best-sellers even though the goal might be to recommend more esoteric titles Z. In this paper, we provide instance-dependent lower bounds for the transductive setting, an algorithm that matches these up to logarithmic factors, and an evaluation. In particular, we provide the first non-asymptotic algorithm for linear bandits that nearly achieves the information theoretic lower bound.
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