In clustering problems, a central decision-maker is given a complete metric graph over vertices and must provide a clustering of vertices that minimizes some objective function. In fair clustering problems, vertices are endowed with a color (e.g., membership in a group), and the features of a valid clustering might also include the representation of colors in that clustering. Prior work in fair clustering assumes complete knowledge of group membership. In this paper, we generalize prior work by assuming imperfect knowledge of group membership through probabilistic assignments. We present clustering algorithms in this more general setting with approximation ratio guarantees. We also address the problem of "metric membership", where different groups have a notion of order and distance. Experiments are conducted using our proposed algorithms as well as baselines to validate our approach and also surface nuanced concerns when group membership is not known deterministically.

We present an improved method for symbolic regression that seeks to fit data to formulas that are Pareto-optimal, in the sense of having the best accuracy for a given complexity. It improves on the previous state-of-the-art by typically being orders of magnitude more robust toward noise and bad data, and also by discovering many formulas that stumped previous methods. We develop a method for discovering generalized symmetries (arbitrary modularity in the computational graph of a formula) from gradient properties of a neural network fit. We use normalizing flows to generalize our symbolic regression method to probability distributions from which we only have samples, and employ statistical hypothesis testing to accelerate robust brute-force search.

In the paper, the new approach to the scheduling problem are described. The approach deals with the problem of planning the cyclic production and proposes to consider such scheduling problem as the cyclic job-shop problem of the order k, where k is the number of reiterations. It was found out that planning of only one iteration of the loop is less effective than planning of the entire cycle. To the experimental research, a number of test instances of the job-shop scheduling problem by Operation Research Library were used. The Simulated Annealing was applied to solve the instances. The experiments proved that the approach proposed allows increasing the efficiency of cyclic scheduling significantly.

Smart devices in the Internet of Things (IoT) paradigm provide a variety of unobtrusive and pervasive means for continuous monitoring of bio-metrics and health information. Furthermore, automated personalization and authentication through such smart systems can enable better user experience and security. In this paper, simultaneous estimation and monitoring of body mass index (BMI) and user identity recognition through a unified machine learning framework using smart beds is explored. To this end, we utilize pressure data collected from textile-based sensor arrays integrated onto a mattress to estimate the BMI values of subjects and classify their identities in different positions by using a deep multitask neural network. First, we filter and extract 14 features from the data and subsequently employ deep neural networks for BMI estimation and subject identification on two different public datasets. Finally, we demonstrate that our proposed solution outperforms prior works and several machine learning benchmarks by a considerable margin, while also estimating users' BMI in a 10-fold cross-validation scheme.

As a mechanism for devices to update a global model without sharing data, federated learning bridges the tension between the need for data and respect for privacy. However, classic FL methods like Federated Averaging struggle with non-iid data, a prevalent situation in the real world. Previous solutions are sub-optimal as they either employ a small shared global subset of data or greater number of models with increased communication costs. We propose FedFMC (Fork-Merge-Consolidate), a method that dynamically forks devices into updating different global models then merges and consolidates separate models into one. We first show the soundness of FedFMC on simple datasets, then run several experiments comparing against baseline approaches. These experiments show that FedFMC substantially improves upon earlier approaches to non-iid data in the federated learning context without using a globally shared subset of data nor increase communication costs.

Recent defenses published at venues like NIPS, ICML, ICLR and CVPR are mainly focused on mitigating white-box attacks. These defenses do not properly consider adaptive adversaries. In this paper, we expand the scope of these defenses to include adaptive black-box adversaries. Our evaluation is done on nine defenses including Barrage of Random Transforms, ComDefend, Ensemble Diversity, Feature Distillation, The Odds are Odd, Error Correcting Codes, Distribution Classifier Defense, K-Winner Take All and Buffer Zones. Our investigation is done using two black-box adversarial models and six widely studied adversarial attacks for CIFAR-10 and Fashion-MNIST datasets. Our analyses show most recent defenses provide only marginal improvements in security, as compared to undefended networks. Based on these results, we propose new standards for properly evaluating defenses to black-box adversaries. We provide this security framework to assist researchers in developing future black-box resistant models.

We study probabilistic safety for Bayesian Neural Networks (BNNs) under adversarial input perturbations. Given a compact set of input points, $T \subseteq \mathbb{R}^m$, we study the probability w.r.t. the BNN posterior that all the points in $T$ are mapped to the same region $S$ in the output space. In particular, this can be used to evaluate the probability that a network sampled from the BNN is vulnerable to adversarial attacks. We rely on relaxation techniques from non-convex optimization to develop a method for computing a lower bound on probabilistic safety for BNNs, deriving explicit procedures for the case of interval and linear function propagation techniques. We apply our methods to BNNs trained on a regression task, airborne collision avoidance, and MNIST, empirically showing that our approach allows one to certify probabilistic safety of BNNs with millions of parameters.

Robust Subspace Recovery (RoSuRe) algorithm was recently introduced as a principled and numerically efficient algorithm that unfolds underlying Unions of Subspaces (UoS) structure, present in the data. The union of Subspaces (UoS) is capable of identifying more complex trends in data sets than simple linear models. We build on and extend RoSuRe to prospect the structure of different data modalities individually. We propose a novel multi-modal data fusion approach based on group sparsity which we refer to as Robust Group Subspace Recovery (RoGSuRe). Relying on a bi-sparsity pursuit paradigm and non-smooth optimization techniques, the introduced framework learns a new joint representation of the time series from different data modalities, respecting an underlying UoS model. We subsequently integrate the obtained structures to form a unified subspace structure. The proposed approach exploits the structural dependencies between the different modalities data to cluster the associated target objects. The resulting fusion of the unlabeled sensors' data from experiments on audio and magnetic data has shown that our method is competitive with other state of the art subspace clustering methods. The resulting UoS structure is employed to classify newly observed data points, highlighting the abstraction capacity of the proposed method.

A core challenge in policy optimization in competitive Markov decision processes is the design of efficient optimization methods with desirable convergence and stability properties. To tackle this, we propose competitive policy optimization (CoPO), a novel policy gradient approach that exploits the game-theoretic nature of competitive games to derive policy updates. Motivated by the competitive gradient optimization method, we derive a bilinear approximation of the game objective. In contrast, off-the-shelf policy gradient methods utilize only linear approximations, and hence do not capture interactions among the players. We instantiate CoPO in two ways:(i) competitive policy gradient, and (ii) trust-region competitive policy optimization. We theoretically study these methods, and empirically investigate their behavior on a set of comprehensive, yet challenging, competitive games. We observe that they provide stable optimization, convergence to sophisticated strategies, and higher scores when played against baseline policy gradient methods.

We initiate the study of applications of machine learning to Seiberg duality, focusing on the case of quiver gauge theories, a problem also of interest in mathematics in the context of cluster algebras. Within the general theme of Seiberg duality, we define and explore a variety of interesting questions, broadly divided into the binary determination of whether a pair of theories picked from a series of duality classes are dual to each other, as well as the multi-class determination of the duality class to which a given theory belongs. We study how the performance of machine learning depends on several variables, including number of classes and mutation type (finite or infinite). In addition, we evaluate the relative advantages of Naive Bayes classifiers versus Convolutional Neural Networks. Finally, we also investigate how the results are affected by the inclusion of additional data, such as ranks of gauge/flavor groups and certain variables motivated by the existence of underlying Diophantine equations. In all questions considered, high accuracy and confidence can be achieved.