We propose and analyze a novel accelerated primal-dual coordinate descent framework for computing the optimal transport (OT) distance between two discrete probability distributions. First, we introduce the accelerated primal-dual randomized coordinate descent (APDRCD) algorithm for computing OT. Then we provide a complexity upper bound $\widetilde{\mathcal{O}}(\frac{n^{5/2}}{\varepsilon})$ for the APDRCD method for approximating OT distance, where $n$ stands for the number of atoms of these probability measures and $\varepsilon > 0$ is the desired accuracy. This upper bound matches the best known complexities of adaptive primal-dual accelerated gradient descent (APDAGD) and adaptive primal-dual accelerate mirror descent (APDAMD) algorithms while it is better than those of Sinkhorn and Greenkhorn algorithms, which are of the order $\widetilde{\mathcal{O}}(\frac{n^{2}}{\varepsilon^2})$, in terms of the desired accuracy $\varepsilon > 0$. Furthermore, we propose a greedy version of APDRCD algorithm that we refer to as the accelerated primal-dual greedy coordinate descent (APDGCD) algorithm and demonstrate that it has a better practical performance than the APDRCD algorithm. Extensive experimental studies demonstrate the favorable performance of the APDRCD and APDGCD algorithms over state-of-the-art primal-dual algorithms for OT in the literature.

Despite recent successes in Reinforcement Learning, value-based methods often suffer from high variance hindering performance. In this paper, we illustrate this in a continuous control setting where state of the art methods perform poorly whenever sensor noise is introduced. To overcome this issue, we introduce Recurrent Value Functions (RVFs) as an alternative to estimate the value function of a state. We propose to estimate the value function of the current state using the value function of past states visited along the trajectory. Due to the nature of their formulation, RVFs have a natural way of learning an emphasis function that selectively emphasizes important states. First, we establish RVF's asymptotic convergence properties in tabular settings. We then demonstrate their robustness on a partially observable domain and continuous control tasks. Finally, we provide a qualitative interpretation of the learned emphasis function.

We consider the problem of binary classification with abstention in the relatively less studied \emph{bounded-rate} setting. We begin by obtaining a characterization of the Bayes optimal classifier for an arbitrary input-label distribution $P_{XY}$. Our result generalizes and provides an alternative proof for the result first obtained by \cite{chow1957optimum}, and then re-derived by \citet{denis2015consistency}, under a continuity assumption on $P_{XY}$. We then propose a plug-in classifier that employs unlabeled samples to decide the region of abstention and derive an upper-bound on the excess risk of our classifier under standard \emph{H\"older smoothness} and \emph{margin} assumptions. Unlike the plug-in rule of \citet{denis2015consistency}, our constructed classifier satisfies the abstention constraint with high probability and can also deal with discontinuities in the empirical cdf. We also derive lower-bounds that demonstrate the minimax near-optimality of our proposed algorithm. To address the excessive complexity of the plug-in classifier in high dimensions, we propose a computationally efficient algorithm that builds upon prior work on convex loss surrogates, and obtain bounds on its excess risk in the \emph{realizable} case. We empirically compare the performance of the proposed algorithm with a baseline on a number of UCI benchmark datasets.

The performance of deep neural networks (DNN) is very sensitive to the particular choice of hyper-parameters. To make it worse, the shape of the learning curve can be significantly affected when a technique like batchnorm is used. As a result, hyperparameter optimization of deep networks can be much more challenging than traditional machine learning models. In this work, we start from well known Bayesian Optimization solutions and provide enhancement strategies specifically designed for hyperparameter optimization of deep networks. The resulting algorithm is named as DEEP-BO (Diversified, Early-termination-Enabled, and Parallel Bayesian Optimization). When evaluated over six DNN benchmarks, DEEP-BO easily outperforms or shows comparable performance with some of the well-known solutions including GP-Hedge, Hyperband, BOHB, Median Stopping Rule, and Learning Curve Extrapolation.

Predictive process monitoring is a family of techniques to analyze events produced during the execution of a business process in order to predict the future state or the final outcome of running process instances. Existing techniques in this field are able to predict, at each step of a process instance, the likelihood that it will lead to an undesired outcome.These techniques, however, focus on generating predictions and do not prescribe when and how process workers should intervene to decrease the cost of undesired outcomes. This paper proposes a framework for prescriptive process monitoring, which extends predictive monitoring with the ability to generate alarms that trigger interventions to prevent an undesired outcome or mitigate its effect. The framework incorporates a parameterized cost model to assess the cost-benefit trade-off of generating alarms. We show how to optimize the generation of alarms given an event log of past process executions and a set of cost model parameters. The proposed approaches are empirically evaluated using a range of real-life event logs. The experimental results show that the net cost of undesired outcomes can be minimized by changing the threshold for generating alarms, as the process instance progresses. Moreover, introducing delays for triggering alarms, instead of triggering them as soon as the probability of an undesired outcome exceeds a threshold, leads to lower net costs.

We propose a new scalable multi-class Gaussian process classification approach building on a novel modified softmax likelihood function. The new likelihood has two benefits: it leads to well-calibrated uncertainty estimates and allows for an efficient latent variable augmentation. The augmented model has the advantage that it is conditionally conjugate leading to a fast variational inference method via block coordinate ascent updates. Previous approaches suffered from a trade-off between uncertainty calibration and speed. Our experiments show that our method leads to well-calibrated uncertainty estimates and competitive predictive performance while being up to two orders faster than the state of the art.

Glioma grading before the surgery is very critical for the prognosis prediction and treatment plan making. In this paper, we present a novel scattering wavelet-based radiomics method to predict noninvasively and accurately the glioma grades. The multimodal magnetic resonance images of 285 patients were used, with the intratumoral and peritumoral regions well labeled. The wavelet scattering-based features and traditional radiomics features were firstly extracted from both intratumoral and peritumoral regions respectively. The support vector machine (SVM), logistic regression (LR) and random forest (RF) were then trained with 5-fold cross validation to predict the glioma grades. The prediction obtained with different features was finally evaluated in terms of quantitative metrics. The area under the receiver operating characteristic curve (AUC) of glioma grade prediction based on scattering wavelet features was up to 0.99 when considering both intratumoral and peritumoral features in multimodal images, which increases by about 17% compared to traditional radiomics. Such results shown that the local invariant features extracted from the scattering wavelet transform allows improving the prediction accuracy for glioma grading. In addition, the features extracted from peritumoral regions further increases the accuracy of glioma grading.

Recent years have witnessed growing interests in designing efficient neural networks and neural architecture search (NAS). Although remarkable efficiency and accuracy have been achieved, existing expert designed and NAS models neglect the fact that input instances are of varying complexity thus different amount of computation is required. Inference with a fixed model that processes all instances through the same transformations would waste plenty of computational resources. Therefore, customizing the model capacity in an instance-aware manner is highly demanded. To address this issue, we propose an Instance-aware Selective Branching Network-ISBNet, which supports efficient instance-level inference by selectively bypassing transformation branches of insignificant importance weight. These weights are determined dynamically by accompanying lightweight hypernetworks SelectionNets and further recalibrated by gumbel-softmax for sparse branch selection. Extensive experiments show that ISBNet achieves extremely efficient inference in terms of parameter size and FLOPs comparing to existing networks. For example, ISBNet takes only 8.03% parameters and 30.60% FLOPs of the state-of-the-art efficient network ShuffleNetV2 with comparable accuracy.

Neural network training is usually accomplished by solving a non-convex optimization problem using stochastic gradient descent. Although one optimizes over the networks parameters, the loss function generally only depends on the realization of a neural network, i.e. the function it computes. Studying the functional optimization problem over the space of realizations can open up completely new ways to understand neural network training. In particular, usual loss functions like the mean squared error are convex on sets of neural network realizations, which themselves are non-convex. Note, however, that each realization has many different, possibly degenerate, parametrizations. In particular, a local minimum in the parametrization space needs not correspond to a local minimum in the realization space. To establish such a connection, inverse stability of the realization map is required, meaning that proximity of realizations must imply proximity of corresponding parametrizations. In this paper we present pathologies which prevent inverse stability in general, and proceed to establish a restricted set of parametrizations on which we have inverse stability w.r.t. to a Sobolev norm. Furthermore, we show that by optimizing over such restricted sets, it is still possible to learn any function, which can be learned by optimization over unrestricted sets. While most of this paper focuses on shallow networks, none of methods used are, in principle, limited to shallow networks, and it should be possible to extend them to deep neural networks.

State-of-the-art deep learning methods have shown a remarkable capacity to model complex data domains, but struggle with geospatial data. In this paper, we introduce SpaceGAN, a novel generative model for geospatial domains that learns neighbourhood structures through spatial conditioning. We propose to enhance spatial representation beyond mere spatial coordinates, by conditioning each data point on feature vectors of its spatial neighbours, thus allowing for a more flexible representation of the spatial structure. To overcome issues of training convergence, we employ a metric capturing the loss in local spatial autocorrelation between real and generated data as stopping criterion for SpaceGAN parametrization. This way, we ensure that the generator produces synthetic samples faithful to the spatial patterns observed in the input. SpaceGAN is successfully applied for data augmentation and outperforms compared to other methods of synthetic spatial data generation. Finally, we propose an ensemble learning framework for the geospatial domain, taking augmented SpaceGAN samples as training data for a set of ensemble learners. We empirically show the superiority of this approach over conventional ensemble learning approaches and rivaling spatial data augmentation methods, using synthetic and real-world prediction tasks. Our findings suggest that SpaceGAN can be used as a tool for (1) artificially inflating sparse geospatial data and (2) improving generalization of geospatial models.