Deep neural networks (DNNs) are notorious for making more mistakes for the classes that have substantially fewer samples than the others during training. Such class imbalance is ubiquitous in clinical applications and very crucial to handle because the classes with fewer samples most often correspond to critical cases (e.g., cancer) where misclassifications can have severe consequences. Not to miss such cases, binary classifiers need to be operated at high True Positive Rates (TPR) by setting a higher threshold but this comes at the cost of very high False Positive Rates (FPR) for problems with class imbalance. Existing methods for learning under class imbalance most often do not take this into account. We argue that prediction accuracy should be improved by emphasizing reducing FPRs at high TPRs for problems where misclassification of the positive samples are associated with higher cost. To this end, we pose the training of a DNN for binary classification as a constrained optimization problem and introduce a novel constraint that can be used with existing loss functions to enforce maximal area under the ROC curve (AUC). We solve the resulting constrained optimization problem using an Augmented Lagrangian method (ALM), where the constraint emphasizes reduction of FPR at high TPR. We present experimental results for image-based classification applications using the CIFAR10 and an in-house medical imaging dataset. Our results demonstrate that the proposed method almost always improves the loss functions it is used with by attaining lower FPR at high TPR and higher or equal AUC.

We consider the zeroth-order optimization problem in the huge-scale setting, where the dimension of the problem is so large that performing even basic vector operations on the decision variables is infeasible. In this paper, we propose a novel algorithm, coined ZO-BCD, that exhibits favorable overall query complexity and has a much smaller per-iteration computational complexity. In addition, we discuss how the memory footprint of ZO-BCD can be reduced even further by the clever use of circulant measurement matrices. As an application of our new method, we propose the idea of crafting adversarial attacks on neural network based classifiers in a wavelet domain, which can result in problem dimensions of over 1.7 million. In particular, we show that crafting adversarial examples to audio classifiers in a wavelet domain can achieve the state-of-the-art attack success rate of 97.9%.

It is argued that a broad class of AGI-relevant algorithms can be expressed in a common formal framework, via specifying Galois connections linking search and optimization processes on directed metagraphs whose edge targets are labeled with probabilistic dependent types, and then showing these connections are fulfilled by processes involving metagraph chronomorphisms. Examples are drawn from the core cognitive algorithms used in the OpenCog AGI framework: Probabilistic logical inference, evolutionary program learning, pattern mining, agglomerative clustering, pattern mining and nonlinear-dynamical attention allocation. The analysis presented involves representing these cognitive algorithms as recursive discrete decision processes involving optimizing functions defined over metagraphs, in which the key decisions involve sampling from probability distributions over metagraphs and enacting sets of combinatory operations on selected sub-metagraphs. The mutual associativity of the combinatory operations involved in a cognitive process is shown to often play a key role in enabling the decomposition of the process into folding and unfolding operations; a conclusion that has some practical implications for the particulars of cognitive processes, e.g. militating toward use of reversible logic and reversible program execution. It is also observed that where this mutual associativity holds, there is an alignment between the hierarchy of subgoals used in recursive decision process execution and a hierarchy of subpatterns definable in terms of formal pattern theory.

In this paper, we investigate the constraint typology of mixed-integer linear programming MILP formulations. MILP is a commonly used mathematical programming technique for modelling and solving real-life scheduling, routing, planning, resource allocation, timetabling optimization problems, providing optimized business solutions for industry sectors such as: manufacturing, agriculture, defence, healthcare, medicine, energy, finance, and transportation. Despite the numerous real-life Combinatorial Optimization Problems found and solved, and millions yet to be discovered and formulated, the number of types of constraints, the building blocks of a MILP, is relatively much smaller. In the search of a suitable machine readable knowledge representation for MILPs, we propose an optimization modelling tree built based upon an MILP ontology that can be used as a guidance for automated systems to elicit an MILP model from end-users on their combinatorial business optimization problems.

We consider a discounted infinite horizon optimal stopping problem. If the underlying distribution is known a priori, the solution of this problem is obtained via dynamic programming (DP) and is given by a well known threshold rule. When information on this distribution is lacking, a natural (though naive) approach is "explore-then-exploit," whereby the unknown distribution or its parameters are estimated over an initial exploration phase, and this estimate is then used in the DP to determine actions over the residual exploitation phase. We show: (i) with proper tuning, this approach leads to performance comparable to the full information DP solution; and (ii) despite common wisdom on the sensitivity of such "plug in" approaches in DP due to propagation of estimation errors, a surprisingly "short" (logarithmic in the horizon) exploration horizon suffices to obtain said performance. In cases where the underlying distribution is heavy-tailed, these observations are even more pronounced: a ${\it single \, sample}$ exploration phase suffices.

In this paper, a mixed-integer linear programming formulation for the problem of obtaining task-relevant, multi-resolution, graph abstractions for resource-constrained agents is presented. The formulation leverages concepts from information-theoretic signal compression, specifically the information bottleneck (IB) method, to pose a graph abstraction problem as an optimal encoder search over the space of multi-resolution trees. The abstractions emerge in a task-relevant manner as a function of agent information-processing constraints, and are not provided to the system a priori. We detail our formulation and show how the problem can be realized as an integer linear program. A non-trivial numerical example is presented to demonstrate the utility in employing our approach to obtain hierarchical tree abstractions for resource-limited agents.

The Vehicle Routing Problem (VRP) is one of the most intensively studied combinatorial optimisation problems for which numerous models and algorithms have been proposed. To tackle the complexities, uncertainties and dynamics involved in real-world VRP applications, Machine Learning (ML) methods have been used in combination with analytical approaches to enhance problem formulations and algorithmic performance across different problem solving scenarios. However, the relevant papers are scattered in several traditional research fields with very different, sometimes confusing, terminologies. This paper presents a first, comprehensive review of hybrid methods that combine analytical techniques with ML tools in addressing VRP problems. Specifically, we review the emerging research streams on ML-assisted VRP modelling and ML-assisted VRP optimisation. We conclude that ML can be beneficial in enhancing VRP modelling, and improving the performance of algorithms for both online and offline VRP optimisations. Finally, challenges and future opportunities of VRP research are discussed.

Robotic fabric manipulation has applications in home robotics, textiles, senior care and surgery. Existing fabric manipulation techniques, however, are designed for specific tasks, making it difficult to generalize across different but related tasks. We build upon the Visual Foresight framework to learn fabric dynamics that can be efficiently reused to accomplish different sequential fabric manipulation tasks with a single goal-conditioned policy. We extend our earlier work on VisuoSpatial Foresight (VSF), which learns visual dynamics on domain randomized RGB images and depth maps simultaneously and completely in simulation. In this earlier work, we evaluated VSF on multi-step fabric smoothing and folding tasks against 5 baseline methods in simulation and on the da Vinci Research Kit (dVRK) surgical robot without any demonstrations at train or test time. A key finding was that depth sensing significantly improves performance: RGBD data yields an 80% improvement in fabric folding success rate in simulation over pure RGB data. In this work, we vary 4 components of VSF, including data generation, the choice of visual dynamics model, cost function, and optimization procedure. Results suggest that training visual dynamics models using longer, corner-based actions can improve the efficiency of fabric folding by 76% and enable a physical sequential fabric folding task that VSF could not previously perform with 90% reliability. Code, data, videos, and supplementary material are available at https://sites.google.com/view/fabric-vsf/.

Nowadays, combinatorial optimization (CO) is an interdisciplinary field spanning optimization, operations research, discrete mathematics, and computer science, with many critical real-world applications such as vehicle routing or scheduling; see [71] for a general overview. Intuitively, CO deals with selecting a subset from a finite set that optimizes a cost or objective function. Although many CO problems are hard from a complexity theory standpoint due to their discrete nature, many of them are routinely solved in practice. Historically, the optimization and theoretical computer science communities have been focusing on finding optimal [71], heuristic [12], or approximative [130] solutions for individual problem instances. However, in many practical situations of interest, one often needs to solve problem instances which share patterns and characteristics repeatedly.

We devise a theoretical framework and a numerical method to infer trajectories of a stochastic process from snapshots of its temporal marginals. This problem arises in the analysis of single cell RNA-sequencing data, which provide high dimensional measurements of cell states but cannot track the trajectories of the cells over time. We prove that for a class of stochastic processes it is possible to recover the ground truth trajectories from limited samples of the temporal marginals at each time-point, and provide an efficient algorithm to do so in practice. The method we develop, Global Waddington-OT (gWOT), boils down to a smooth convex optimization problem posed globally over all time-points involving entropy-regularized optimal transport. We demonstrate that this problem can be solved efficiently in practice and yields good reconstructions, as we show on several synthetic and real datasets.