Learning Acceptance Regions for Many Classes with Anomaly Detection

Set-valued classification, a new classification paradigm that aims to identify all the plausible classes that an observation belongs to, can be obtained by learning the acceptance regions for all classes. Many existing set-valued classification methods do not consider the possibility that a new class that never appeared in the training data appears in the test data. Moreover, they are computationally expensive when the number of classes is large. We propose a Generalized Prediction Set (GPS) approach to estimate the acceptance regions while considering the possibility of a new class in the test data. The proposed classifier minimizes the expected size of the prediction set while guaranteeing that the class-specific accuracy is at least a pre-specified value. Unlike previous methods, the proposed method achieves a good balance between accuracy, efficiency, and anomaly detection rate. Moreover, our method can be applied in parallel to all the classes to alleviate the computational burden. Both theoretical analysis and numerical experiments are conducted to illustrate the effectiveness of the proposed method.

Enhanced Nearest Neighbor Classification for Crowdsourcing

In machine learning, crowdsourcing is an economical way to label a large amount of data. However, the noise in the produced labels may deteriorate the accuracy of any classification method applied to the labelled data. We propose an enhanced nearest neighbor classifier (ENN) to overcome this issue. Two algorithms are developed to estimate the worker quality (which is often unknown in practice): one is to construct the estimate based on the denoised worker labels by applying the $k$NN classifier to the expert data; the other is an iterative algorithm that works even without access to the expert data. Other than strong numerical evidence, our proposed methods are proven to achieve the same regret as its oracle version based on high-quality expert data. As a technical by-product, a lower bound on the sample size assigned to each worker to reach the optimal convergence rate of regret is derived.

Covariance-engaged Classification of Sets via Linear Programming

Set classification aims to classify a set of observations as a whole, as opposed to classifying individual observations separately. To formally understand the unfamiliar concept of binary set classification, we first investigate the optimal decision rule under the normal distribution, which utilizes the empirical covariance of the set to be classified. We show that the number of observations in the set plays a critical role in bounding the Bayes risk. Under this framework, we further propose new methods of set classification. For the case where only a few parameters of the model drive the difference between two classes, we propose a computationally-efficient approach to parameter estimation using linear programming, leading to the Covariance-engaged LInear Programming Set (CLIPS) classifier. Its theoretical properties are investigated for both independent case and various (short-range and long-range dependent) time series structures among observations within each set. The convergence rates of estimation errors and risk of the CLIPS classifier are established to show that having multiple observations in a set leads to faster convergence rates, compared to the standard classification situation in which there is only one observation in the set. The applicable domains in which the CLIPS performs better than competitors are highlighted in a comprehensive simulation study. Finally, we illustrate the usefulness of the proposed methods in classification of real image data in histopathology.

Near-optimal Individualized Treatment Recommendations

Individualized treatment recommendation (ITR) is an important analytic framework for precision medicine. The goal is to assign proper treatments to patients based on their individual characteristics. From the machine learning perspective, the solution to an ITR problem can be formulated as a weighted classification problem to maximize the average benefit that patients receive from the recommended treatments. Several methods have been proposed for ITR in both binary and multicategory treatment setups. In practice, one may prefer a more flexible recommendation with multiple treatment options. This motivates us to develop methods to obtain a set of near-optimal individualized treatment recommendations alternative to each other, called alternative individualized treatment recommendations (A-ITR). We propose two methods to estimate the optimal A-ITR within the outcome weighted learning (OWL) framework. We show the consistency of these methods and obtain an upper bound for the risk between the theoretically optimal recommendation and the estimated one. We also conduct simulation studies, and apply our methods to a real data set for Type 2 diabetic patients with injectable antidiabetic treatments. These numerical studies have shown the usefulness of the proposed A-ITR framework. We develop a R package aitr which can be found at https://github.com/menghaomiao/aitr.

Maximum Entropy Diverse Exploration: Disentangling Maximum Entropy Reinforcement Learning

Two hitherto disconnected threads of research, diverse exploration (DE) and maximum entropy RL have addressed a wide range of problems facing reinforcement learning algorithms via ostensibly distinct mechanisms. In this work, we identify a connection between these two approaches. First, a discriminator-based diversity objective is put forward and connected to commonly used divergence measures. We then extend this objective to the maximum entropy framework and propose an algorithm Maximum Entropy Diverse Exploration (MEDE) which provides a principled method to learn diverse behaviors. A theoretical investigation shows that the set of policies learned by MEDE capture the same modalities as the optimal maximum entropy policy. In effect, the proposed algorithm disentangles the maximum entropy policy into its diverse, constituent policies. Experiments show that MEDE is superior to the state of the art in learning high performing and diverse policies.

Rates of Convergence for Large-scale Nearest Neighbor Classification

Nearest neighbor is a popular class of classification methods with many desirable properties. For a large data set which cannot be loaded into the memory of a single machine due to computation, communication, privacy, or ownership limitations, we consider the divide and conquer scheme: the entire data set is divided into small subsamples, on which nearest neighbor predictions are made, and then a final decision is reached by aggregating the predictions on subsamples by majority voting. We name this method the big Nearest Neighbor (bigNN) classifier, and provide its rates of convergence under minimal assumptions, in terms of both the excess risk and the classification instability, which are proven to be the same rates as the oracle nearest neighbor classifier and cannot be improved. To significantly reduce the prediction time that is required for achieving the optimal rate, we also consider the pre-training acceleration technique applied to the bigNN method, with proven convergence rate. We find that in the distributed setting, the optimal choice of the neighbor k should scale with both the total sample size and the number of partitions, and there is a theoretical upper limit for the latter. Numerical studies have verified the theoretical findings.

Towards Run Time Estimation of the Gaussian Chemistry Code for SEAGrid Science Gateway

Accurate estimation of the run time of computational codes has a number of significant advantages for scientific computing. It is required information for optimal resource allocation, improving turnaround times and utilization of science gateways. Furthermore, it allows users to better plan and schedule their research, streamlining workflows and improving the overall productivity of cyberinfrastructure. Predicting run time is challenging, however. The inputs to scientific codes can be complex and high dimensional. Their relationship to the run time may be highly non-linear, and, in the most general case is completely arbitrary and thus unpredictable (i.e., simply a random mapping from inputs to run time). Most codes are not so arbitrary, however, and there has been significant prior research on predicting the run time of applications and workloads. Such predictions are generally application-specific, however. In this paper, we focus on the Gaussian computational chemistry code. We characterize a data set of runs from the SEAGrid science gateway with a number of different studies. We also explore a number of different potential regression methods and present promising future directions.

Diverse Exploration via Conjugate Policies for Policy Gradient Methods

We address the challenge of effective exploration while maintaining good performance in policy gradient methods. As a solution, we propose diverse exploration (DE) via conjugate policies. DE learns and deploys a set of conjugate policies which can be conveniently generated as a byproduct of conjugate gradient descent. We provide both theoretical and empirical results showing the effectiveness of DE at achieving exploration, improving policy performance, and the advantage of DE over exploration by random policy perturbations.

Learning Confidence Sets using Support Vector Machines

The goal of confidence-set learning in the binary classification setting is to construct two sets, each with a specific probability guarantee to cover a class. An observation outside the overlap of the two sets is deemed to be from one of the two classes, while the overlap is an ambiguity region which could belong to either class. Instead of plug-in approaches, we propose a support vector classifier to construct confidence sets in a flexible manner. Theoretically, we show that the proposed learner can control the non-coverage rates and minimize the ambiguity with high probability. Efficient algorithms are developed and numerical studies illustrate the effectiveness of the proposed method.

On Reject and Refine Options in Multicategory Classification

In many real applications of statistical learning, a decision made from misclassification can be too costly to afford; in this case, a reject option, which defers the decision until further investigation is conducted, is often preferred. In recent years, there has been much development for binary classification with a reject option. Yet, little progress has been made for the multicategory case. In this article, we propose margin-based multicategory classification methods with a reject option. In addition, and more importantly, we introduce a new and unique refine option for the multicategory problem, where the class of an observation is predicted to be from a set of class labels, whose cardinality is not necessarily one. The main advantage of both options lies in their capacity of identifying error-prone observations. Moreover, the refine option can provide more constructive information for classification by effectively ruling out implausible classes. Efficient implementations have been developed for the proposed methods. On the theoretical side, we offer a novel statistical learning theory and show a fast convergence rate of the excess $\ell$-risk of our methods with emphasis on diverging dimensionality and number of classes. The results can be further improved under a low noise assumption. A set of comprehensive simulation and real data studies has shown the usefulness of the new learning tools compared to regular multicategory classifiers. Detailed proofs of theorems and extended numerical results are included in the supplemental materials available online.