We present a unified view of three different problems; rank reduction of matrices, matrix balancing, and mean-field approximation, using information geometry. Our key idea is to treat each matrix as a probability distribution represented by a loglinear model on a partially ordered set (poset), which enables us to formulate rank reduction and balancing of a matrix as projection onto a statistical submanifold, which corresponds to the set of low-rank matrices or that of balanced matrices. Moreover, the process of rank-1 reduction coincides with the mean-field approximation in the sense that the expectation parameters can be decomposed into products, where the mean-field equation holds. Our observation leads to a new convex optimization formulation of rank reduction, which applies to any nonnegative matrices, while the Nystr\"om method, one of the most popular rank reduction methods, is applicable to only kernel positive semidefinite matrices. We empirically show that our rank reduction method achieves better approximation of matrices produced by real-world data compared to Nystrom method.

Early recognition of clinical deterioration is one of the main steps for reducing inpatient morbidity and mortality. The challenging task of clinical deterioration identification in hospitals lies in the intense daily routines of healthcare practitioners, in the unconnected patient data stored in the Electronic Health Records (EHRs) and in the usage of low accuracy scores. Since hospital wards are given less attention compared to the Intensive Care Unit, ICU, we hypothesized that when a platform is connected to a stream of EHR, there would be a drastic improvement in dangerous situations awareness and could thus assist the healthcare team. With the application of machine learning, the system is capable to consider all patient's history and through the use of high-performing predictive models, an intelligent early warning system is enabled. In this work we used 121,089 medical encounters from six different hospitals and 7,540,389 data points, and we compared popular ward protocols with six different scalable machine learning methods (three are classic machine learning models, logistic and probabilistic-based models, and three gradient boosted models). The results showed an advantage in AUC (Area Under the Receiver Operating Characteristic Curve) of 25 percentage points in the best Machine Learning model result compared to the current state-of-the-art protocols. This is shown by the generalization of the algorithm with leave-one-group-out (AUC of 0.949) and the robustness through cross-validation (AUC of 0.961). We also perform experiments to compare several window sizes to justify the use of five patient timestamps. A sample dataset, experiments, and code are available for replicability purposes.

As learning solutions reach critical applications in social, industrial, and medical domains, the need to curtail their behavior becomes paramount. There is now ample evidence that without explicit tailoring, learning can lead to biased, unsafe, and prejudiced solutions. To tackle these problems, we develop a generalization theory of constrained learning based on the probably approximately correct (PAC) learning framework. In particular, we show that imposing requirements does not make a learning problem harder in the sense that any PAC learnable class is also PAC constrained learnable using a constrained counterpart of the empirical risk minimization (ERM) rule. For typical parametrized models, however, this learner involves solving a non-convex optimization program for which even obtaining a feasible solution may be hard. To overcome this issue, we prove that under mild conditions the empirical dual problem of constrained learning is also a PAC constrained learner that now leads to a practical constrained learning algorithm. We analyze the generalization properties of this solution and use it to illustrate how constrained learning can address problems in fair and robust classification.

We study a version of the classical zero-sum matrix game with unknown payoff matrix and bandit feedback, where the players only observe each others actions and a noisy payoff. This generalizes the usual matrix game, where the payoff matrix is known to the players. Despite numerous applications, this problem has received relatively little attention. Although adversarial bandit algorithms achieve low regret, they do not exploit the matrix structure and perform poorly relative to the new algorithms. The main contributions are regret analyses of variants of UCB and K-learning that hold for any opponent, e.g., even when the opponent adversarially plays the best response to the learner's mixed strategy. Along the way, we show that Thompson fails catastrophically in this setting and provide empirical comparison to existing algorithms.

Improving the robustness of neural nets in regression tasks is key to their application in multiple domains. Deep learning-based approaches aim to achieve this goal either by improving the manner in which they produce their prediction of specific values (i.e., point prediction), or by producing prediction intervals (PIs) that quantify uncertainty. We present PIVEN, a deep neural network for producing both a PI and a prediction of specific values. Benchmark experiments show that our approach produces tighter uncertainty bounds than the current state-of-the-art approach for producing PIs, while managing to maintain comparable performance to the state-of-the-art approach for specific value-prediction. Additional evaluation on large image datasets further support our conclusions.

We study a contextual bandit setting where the learning agent has access to sampled bandit instances from an unknown prior distribution $\mathcal{P}$. The goal of the agent is to achieve high reward on average over the instances drawn from $\mathcal{P}$. This setting is of a particular importance because it formalizes the offline optimization of bandit policies, to perform well on average over anticipated bandit instances. The main idea in our work is to optimize differentiable bandit policies by policy gradients. We derive reward gradients that reflect the structure of our problem, and propose contextual policies that are parameterized in a differentiable way and have low regret. Our algorithmic and theoretical contributions are supported by extensive experiments that show the importance of baseline subtraction, learned biases, and the practicality of our approach on a range of classification tasks.

Deep neural networks can now perform many tasks that were once thought to be only feasible for humans. Unfortunately, while reaching impressive performance under standard settings, such networks are known to be susceptible to adversarial attacks -- slight but carefully constructed perturbations of the inputs which drastically decrease the network performance and reduce their trustworthiness. Here we propose to improve network robustness to input perturbations via an adversarial training procedure which we call Adversarial Feature Desensitization (AFD). We augment the normal supervised training with an adversarial game between the embedding network and an additional adversarial decoder which is trained to discriminate between the clean and perturbed inputs from their high-level embeddings. Our theoretical and empirical evidence acknowledges the effectiveness of this approach in learning robust features on MNIST, CIFAR10, and CIFAR100 datasets -- substantially improving the state-of-the-art in robust classification against previously observed adversarial attacks. More importantly, we demonstrate that AFD has better generalization ability than previous methods, as the learned features maintain their robustness against a large range of perturbations, including perturbations not seen during training. These results indicate that reducing feature sensitivity using adversarial training is a promising approach for ameliorating the problem of adversarial attacks in deep neural networks.

Due to the growing deployment of classification algorithms in various social contexts, developing methods that are fair with respect to protected attributes such as gender or race is an important problem. However, the information about protected attributes in datasets may be inaccurate due to either issues with data collection or when the protected attributes used are themselves predicted by algorithms. Such inaccuracies can prevent existing fair classification algorithms from achieving desired fairness guarantees. Motivated by this, we study fair classification problems when the protected attributes in the data may be ``noisy''. In particular, we consider a noise model where any protected type may be flipped to another with some fixed probability. We propose a ``denoised'' fair optimization formulation that can incorporate very general fairness goals via a set of constraints, mitigates the effects of such noise perturbations, and comes with provable guarantees. Empirically, we show that our framework can lead to near-perfect statistical parity with only a slight loss in accuracy for significant noise levels.

Scheduling and facility location represent two classes of well-studied combinatorial optimization problems. The main motivation for studying them relies on the broad range of applications (e.g., in public services, industry, logistics, project management, production planning, data processing, etc.), as well as on the challenge in providing efficient solutions, since many of these problems are classified as NPhard (see, e.g., Pinedo 2009, Pinedo 2016, Drezner and Hamacher 2002, and Laporte et al. 2015). Since the 1960s, many works on these topics have been published, but only a few of them has focused on studying these problems in an integrated fashion. Due to the limited capacity of the computers of two decades ago, it was usual to solve integrated combinatorial optimization problems using sequential approaches, i.e., solving each problem separately in such a way that the solution of one represents an input to the other. However, this strategy does not guarantee the optimality of the overall solution and, in addition, the input solutions may not be feasible for the successor problems. With the recent advances in technology, especially in the computational field, solving integrated combinatorial optimization problems using integrated approaches is becoming more accessible. In this context, the ScheLoc problem combines the job scheduling and facility location in a single and integrated problem.

There has been an increased need for secondary means of credit evaluation by both traditional banking organizations as well as peer-to-peer lending entities. This is especially important in the present technological era where sticking with strict primary credit histories doesn't help distinguish between a 'good' and a 'bad' borrower, and ends up hurting both the individual borrower as well as the investor as a whole. We utilized machine learning classification and clustering algorithms to accurately predict a borrower's creditworthiness while identifying specific secondary attributes that contribute to this score. While extensive research has been done in predicting when a loan would be fully paid, the area of feature selection for lending is relatively new. We achieved 65% F1 and 73% AUC on the LendingClub data while identifying key secondary attributes.