Although with progress in introducing auxiliary amortized inference models, learning discrete latent variable models is still challenging. In this paper, we show that the annoying difficulty of obtaining reliable stochastic gradients for the inference model and the drawback of indirectly optimizing the target log-likelihood can be gracefully addressed in a new method based on stochastic approximation (SA) theory of the Robbins-Monro type. Specifically, we propose to directly maximize the target log-likelihood and simultaneously minimize the inclusive divergence between the posterior and the inference model. The resulting learning algorithm is called joint SA (JSA). To the best of our knowledge, JSA represents the first method that couples an SA version of the EM (expectation-maximization) algorithm (SAEM) with an adaptive MCMC procedure. Experiments on several benchmark generative modeling and structured prediction tasks show that JSA consistently outperforms recent competitive algorithms, with faster convergence, better final likelihoods, and lower variance of gradient estimates.

Geometric representation learning has recently shown great promise in several machine learning settings, ranging from relational learning to language processing and generative models. In this work, we consider the problem of performing manifold-valued regression onto an hyperbolic space as an intermediate component for a number of relevant machine learning applications. In particular, by formulating the problem of predicting nodes of a tree as a manifold regression task in the hyperbolic space, we propose a novel perspective on two challenging tasks: 1) hierarchical classification via label embeddings and 2) taxonomy extension of hyperbolic representations. To address the regression problem we consider previous methods as well as proposing two novel approaches that are computationally more advantageous: a parametric deep learning model that is informed by the geodesics of the target space and a non-parametric kernel-method for which we also prove excess risk bounds. Our experiments show that the strategy of leveraging the hyperbolic geometry is promising. In particular, in the taxonomy expansion setting, we find that the hyperbolic-based estimators significantly outperform methods performing regression in the ambient Euclidean space.

In this paper, we consider the task of predicting travel times between two arbitrary points in an urban scenario. We view this problem from two temporal perspectives: long-term forecasting with a horizon of several days and short-term forecasting with a horizon of one hour. Both of these perspectives are relevant for planning tasks in the context of urban mobility and transportation services. We utilize tree-based ensemble methods that we train and evaluate on a dataset of taxi trip records from New York City. Through extensive data analysis, we identify relevant temporal and spatial features. We also engineer additional features based on weather and routing data. The latter is obtained via a routing solver operating on the road network. The computational results show that the addition of this routing data can be beneficial to the model performance. Moreover, employing different models for short and long-term prediction is useful as short-term models are better suited to mirror current traffic conditions. In fact, we show that accurate short-term predictions may be obtained with only little training data.

In a landmark paper published in 2001, Leo Breiman described the tense standoff between two cultures of data modeling: parametric statistical and algorithmic machine learning. The cultural division between these two statistical learning frameworks has been growing at a steady pace in recent years. What is the way forward? It has become blatantly obvious that this widening gap between "the two cultures" cannot be averted unless we find a way to blend them into a coherent whole. This article presents a solution by establishing a link between the two cultures. Through examples, we describe the challenges and potential gains of this new integrated statistical thinking.

Causal loop and stock and flow diagrams are broadly used in System Dynamics because they help organize relationships and convey meaning. Using the analytical work of Schoenberg (2019) to select what to include in a compressed model, this paper demonstrates how that information can be clearly presented in an automatically generated causal loop diagram. The diagrams are generated using tools developed by people working in graph theory and the generated diagrams are clear and aesthetically pleasing. This approach can also be built upon to generate stock and flow diagrams. Automated stock and flow diagram generation opens the door to representing models developed using only equations, regardless or origin, in a clear and easy to understand way. Because models can be large, the application of grouping techniques, again developed for graph theory, can help structure the resulting diagrams in the most usable form. This paper describes the algorithms developed for automated diagram generation and shows a number of examples of their uses in large models. The application of these techniques to existing, but inaccessible, equation-based models can help broaden the knowledge base for System Dynamics modeling. The techniques can also be used to improve layout in all, or part, of existing models with diagrammatic informtion.

The increasing demand for democratizing machine learning algorithms for general software developers calls for hyperparameter optimization (HPO) solutions at low cost. Many machine learning algorithms have hyperparameters, which can cause a large variation in the training cost. But this effect is largely ignored in existing HPO methods, which are incapable to properly control cost during the optimization process. To address this problem, we develop a cost effective HPO solution. The core of our solution is a new randomized direct-search method. We prove a convergence rate of $O(\frac{\sqrt{d}}{\sqrt{K}})$ and provide an analysis on how it can be used to control evaluation cost under reasonable assumptions. Extensive evaluation using a latest AutoML benchmark shows a strong any time performance of the proposed HPO method when tuning cost-related hyperparameters.

A latent block model or an LBM [10, 7] has been widely used as a generative model of a relational data matrix, where the rows and columns represent different objects (e.g., customers and items), and its (i, j)-th element shows some relationship between objects i and j (e.g., how many times the customer i purchased item j). Until now, its effectiveness has been shown in various practical datasets, including customer-product transaction relationships [25] and gene expression data [24, 28]. In LBMs, we assume that there is an underlying block structure (i.e., a set of row and column cluster memberships) behind the observed data matrix and that each element of the matrix is generated independently from an identical distribution, given such a block structure. Particularly, a Gaussian LBM [22, 21] is useful to model a relational data matrix with real elements; this type of LBM is the focus of the current study. In a Gaussian LBM, we assume that each entry follows a Gaussian distribution, whose mean and variance are fixed constants in the same block (a formal description of Gaussian LBMs is given in Section 2.1). Besides estimating the block structure from a given observed data matrix based on an LBM, it is also important to test the validity of a model (i.e., the number of blocks) or an estimation result. Until now, several tests [2, 19, 12, 29, 27] have been proposed for determining the number of blocks in block models, such as a stochastic block model (SBM), which is a model for a square symmetric matrix (e.g., an adjacency matrix of the network structure). Among these studies, only [27]'s test can be applied to the LBM setting; however, its target is different from ours in that it is limited to the

Adversarially robust classification seeks a classifier that is insensitive to adversarial perturbations of test patterns. This problem is often formulated via a minimax objective, where the target loss is the worst-case value of the 0-1 loss subject to a bound on the size of perturbation. Recent work has proposed convex surrogates for the adversarial 0-1 loss, in an effort to make optimization more tractable. In this work, we consider the question of which surrogate losses are calibrated with respect to the adversarial 0-1 loss, meaning that minimization of the former implies minimization of the latter. We show that no convex surrogate loss is calibrated with respect to the adversarial 0-1 loss when restricted to the class of linear models. We further introduce a class of nonconvex losses and offer necessary and sufficient conditions for losses in this class to be calibrated.

Recent studies propose membership inference (MI) attacks on deep models. Despite the moderate accuracy of such MI attacks, we show that the way the attack accuracy is reported is often misleading and a simple blind attack which is highly unreliable and inefficient in reality can often represent similar accuracy. We show that the current MI attack models can only identify the membership of misclassified samples with mediocre accuracy at best, which only constitute a very small portion of training samples. We analyze several new features that have not been explored for membership inference before, including distance to the decision boundary and gradient norms, and conclude that deep models' responses are mostly indistinguishable among train and non-train samples. Moreover, in contrast with general intuition that deeper models have a capacity to memorize training samples, and, hence, they are more vulnerable to membership inference, we find no evidence to support that and in some cases deeper models are often harder to launch membership inference attack on. Furthermore, despite the common belief, we show that overfitting does not necessarily lead to higher degree of membership leakage. We conduct experiments on MNIST, CIFAR-10, CIFAR-100, and ImageNet, using various model architecture, including LeNet, ResNet, DenseNet, InceptionV3, and Xception.

Orthogonal Monte Carlo (OMC) is a very effective sampling algorithm imposing structural geometric conditions (orthogonality) on samples for variance reduction. Due to its simplicity and superior performance as compared to its Quasi Monte Carlo counterparts, OMC is used in a wide spectrum of challenging machine learning applications ranging from scalable kernel methods to predictive recurrent neural networks, generative models and reinforcement learning. However theoretical understanding of the method remains very limited. In this paper we shed new light on the theoretical principles behind OMC, applying theory of negatively dependent random variables to obtain several new concentration results. We also propose a novel extensions of the method leveraging number theory techniques and particle algorithms, called Near-Orthogonal Monte Carlo (NOMC). We show that NOMC is the first algorithm consistently outperforming OMC in applications ranging from kernel methods to approximating distances in probabilistic metric spaces.