Dose-finding design based on level set estimation in phase I cancer clinical trials Keiichiro Seno 1 a, Kota Matsui 2b, Shogo Iwazaki 3, Yu Inatsu 4, Shion Takeno 5, 6 and Shigeyuki Matsui 2, 7 1 Department of Biostatistics, Nagoya University 2 Department of Biostatistics, Kyoto University 3 MI-6 Ltd. 4 Department of Computer Science, Nagoya Institute of Technology 5 Department of Mechanical Systems Engineering, Nagoya University 6 Center for Advanced Intelligence Project, RIKEN 7 Research Center for Medical and Health Data Science, The Institute of Statistical Mathematics Abstract The primary objective of phase I cancer clinical trials is to evaluate the safety of a new experimental treatment and to find the maximum tolerated dose (MTD). We show that the MTD estimation problem can be regarded as a level set estimation (LSE) problem whose objective is to determine the regions where an unknown function value is above or below a given threshold. Then, we propose a novel ...

In multiple classification, one aims to determine whether a testing sequence is generated from the same distribution as one of the M training sequences or not. Unlike most of existing studies that focus on discrete-valued sequences with perfect distribution match, we study multiple classification for continuous sequences with distribution uncertainty, where the generating distributions of the testing and training sequences deviate even under the true hypothesis. In particular, we propose distribution free tests and prove that the error probabilities of our tests decay exponentially fast for three different test designs: fixed-length, sequential, and two-phase tests. We first consider the simple case without the null hypothesis, where the testing sequence is known to be generated from a distribution close to the generating distribution of one of the training sequences. Subsequently, we generalize our results to a more general case with the null hypothesis by allowing the testing sequence to be generated from a distribution that is vastly different from the generating distributions of all training sequences.

Real-world applications of machine learning models are often subject to legal or policy-based regulations. Some of these regulations require ensuring the validity of the model, i.e., the approximation error being smaller than a threshold. A global metric is generally too insensitive to determine the validity of a specific prediction, whereas evaluating local validity is costly since it requires gathering additional data.We propose learning the model error to acquire a local validity estimate while reducing the amount of required data through active learning. Using model validation benchmarks, we provide empirical evidence that the proposed method can lead to an error model with sufficient discriminative properties using a relatively small amount of data. Furthermore, an increased sensitivity to local changes of the validity bounds compared to alternative approaches is demonstrated.

Cluster analysis is a popular unsupervised learning tool used in many disciplines to identify heterogeneous sub-populations within a sample. However, validating cluster analysis results and determining the number of clusters in a data set remains an outstanding problem. In this work, we present a global criterion called the Distinguishability criterion to quantify the separability of identified clusters and validate inferred cluster configurations. Our computational implementation of the Distinguishability criterion corresponds to the Bayes risk of a randomized classifier under the 0-1 loss. We propose a combined loss function-based computational framework that integrates the Distinguishability criterion with many commonly used clustering procedures, such as hierarchical clustering, k-means, and finite mixture models. We present these new algorithms as well as the results from comprehensive data analysis based on simulation studies and real data applications.

Classification of high-dimensional low sample size (HDLSS) data poses a challenge in a variety of real-world situations, such as gene expression studies, cancer research, and medical imaging. This article presents the development and analysis of some classifiers that are specifically designed for HDLSS data. These classifiers are free of tuning parameters and are robust, in the sense that they are devoid of any moment conditions of the underlying data distributions. It is shown that they yield perfect classification in the HDLSS asymptotic regime, under some fairly general conditions. The comparative performance of the proposed classifiers is also investigated. Our theoretical results are supported by extensive simulation studies and real data analysis, which demonstrate promising advantages of the proposed classification techniques over several widely recognized methods.

In engineering design, one often wishes to calculate the probability that the performance of a system is satisfactory under uncertainty. State of the art algorithms exist to solve this problem using active learning with Gaussian process models. However, these algorithms cannot be applied to problems which often occur in the autonomous vehicle domain where the performance of a system may be undefined under certain circumstances. To solve this problem, we introduce a hierarchical model for the system performance, where undefined performance is classified before the performance is regressed. This enables active learning Gaussian process methods to be applied to problems where the performance of the system is sometimes undefined, and we demonstrate the effectiveness of our approach by testing our methodology on synthetic numerical examples for the autonomous driving domain.

We propose a distributionally robust support vector machine with a fairness constraint that encourages the classifier to be fair in view of the equality of opportunity criterion. We use a type-$\infty$ Wasserstein ambiguity set centered at the empirical distribution to model distributional uncertainty and derive an exact reformulation for worst-case unfairness measure. We establish that the model is equivalent to a mixed-binary optimization problem, which can be solved by standard off-the-shelf solvers. We further prove that the expectation of the hinge loss objective function constitutes an upper bound on the misclassification probability. Finally, we numerically demonstrate that our proposed approach improves fairness with negligible loss of predictive accuracy.

Statistical methods protecting sensitive information or the identity of the data owner have become critical to ensure privacy of individuals as well as of organizations. This paper investigates anonymization methods based on representation learning and deep neural networks, and motivated by novel information theoretical bounds. We introduce a novel training objective for simultaneously training a predictor over target variables of interest (the regular labels) while preventing an intermediate representation to be predictive of the private labels. The architecture is based on three sub-networks: one going from input to representation, one from representation to predicted regular labels, and one from representation to predicted private labels. The training procedure aims at learning representations that preserve the relevant part of the information (about regular labels) while dismissing information about the private labels which correspond to the identity of a person. We demonstrate the success of this approach for two distinct classification versus anonymization tasks (handwritten digits and sentiment analysis).