Methods for estimating heterogeneous treatment effect in observational data have largely focused on continuous or binary outcomes, and have been relatively less vetted with survival outcomes. Using flexible machine learning methods in the counterfactual framework is a promising approach to address challenges due to complex individual characteristics, to which treatments need to be tailored. To evaluate the operating characteristics of recent survival machine learning methods for the estimation of TEH and inform better practice, we carry out a comprehensive simulation study representing a variety of confounded heterogeneous survival treatment effect settings and varying degrees of covariate overlap. Our results indicate that the nonparametric Bayesian Additive Regression Trees within the framework of accelerated failure time model (AFT-BART-NP) consistently carries the best performance, both in terms of bias and precision. Moreover, the credible interval estimators from AFT-BART-NP provide close to nominal frequentist coverage for the individual survival treatment effect when the covariate overlap is at least moderate. Under lack of overlap, where accurate estimation of the average treatment effect becomes challenging, the credible intervals from AFT-BART-NP still provide nominal frequentist coverage among units near the centroid of the propensity score distribution. Finally, we demonstrate the application of these machine learning methods through a comprehensive case study examining the heterogeneous survival effects of two radiotherapy approaches for localized high-risk prostate cancer.

Multivariate time series modeling and prediction problems are abundant in many machine learning application domains. Accurate interpretation of such prediction outcomes from a machine learning model that explicitly captures temporal correlations can significantly benefit the domain experts. In this context, temporal attention has been successfully applied to isolate the important time steps for the input time series. However, in multivariate time series problems, spatial interpretation is also critical to understand the contributions of different variables on the model outputs. We propose a novel deep learning architecture, called spatiotemporal attention mechanism (STAM) for simultaneous learning of the most important time steps and variables. STAM is a causal (i.e., only depends on past inputs and does not use future inputs) and scalable (i.e., scales well with an increase in the number of variables) approach that is comparable to the state-of-the-art models in terms of computational tractability. We demonstrate our models' performance on two popular public datasets and a domain-specific dataset. When compared with the baseline models, the results show that STAM maintains state-of-the-art prediction accuracy while offering the benefit of accurate spatiotemporal interpretability. The learned attention weights are validated from a domain knowledge perspective for these real-world datasets.

Boolean tensor has been broadly utilized in representing high dimensional logical data collected on spatial, temporal and/or other relational domains. Boolean Tensor Decomposition (BTD) factorizes a binary tensor into the Boolean sum of multiple rank-1 tensors, which is an NP-hard problem. Existing BTD methods have been limited by their high computational cost, in applications to large scale or higher order tensors. In this work, we presented a computationally efficient BTD algorithm, namely \textit{Geometric Expansion for all-order Tensor Factorization} (GETF), that sequentially identifies the rank-1 basis components for a tensor from a geometric perspective. We conducted rigorous theoretical analysis on the validity as well as algorithemic efficiency of GETF in decomposing all-order tensor. Experiments on both synthetic and real-world data demonstrated that GETF has significantly improved performance in reconstruction accuracy, extraction of latent structures and it is an order of magnitude faster than other state-of-the-art methods.

Representation learning of static and more recently dynamically evolving graphs has gained noticeable attention. Existing approaches for modelling graph dynamics focus extensively on the evolution of individual nodes independently of the evolution of mesoscale community structures. As a result, current methods do not provide useful tools to study and cannot explicitly capture temporal community dynamics. To address this challenge, we propose GRADE - a probabilistic model that learns to generate evolving node and community representations by imposing a random walk prior over their trajectories. Our model also learns node community membership which is updated between time steps via a transition matrix. At each time step link generation is performed by first assigning node membership from a distribution over the communities, and then sampling a neighbor from a distribution over the nodes for the assigned community. We parametrize the node and community distributions with neural networks and learn their parameters via variational inference. Experiments demonstrate GRADE outperforms baselines in dynamic link prediction, shows favourable performance on dynamic community detection, and identifies coherent and interpretable evolving communities.

We develop a novel and single-loop variance-reduced algorithm to solve a class of stochastic nonconvex-convex minimax problems involving a nonconvex-linear objective function, which has various applications in different fields such as machine learning and robust optimization. This problem class has several computational challenges due to its nonsmoothness, nonconvexity, nonlinearity, and non-separability of the objective functions. Our approach relies on a new combination of recent ideas, including smoothing and hybrid biased variance-reduced techniques. Our algorithm and its variants can achieve $\mathcal{O}(T^{-2/3})$-convergence rate and the best known oracle complexity under standard assumptions, where $T$ is the iteration counter. They have several computational advantages compared to existing methods such as simple to implement and less parameter tuning requirements. They can also work with both single sample or mini-batch on derivative estimators, and with constant or diminishing step-sizes. We demonstrate the benefits of our algorithms over existing methods through two numerical examples, including a nonsmooth and nonconvex-non-strongly concave minimax model.

Generative Adversarial Networks are notoriously challenging to train. The underlying minmax optimization is highly susceptible to the variance of the stochastic gradient and the rotational component of the associated game vector field. To tackle these challenges, we propose the Lookahead algorithm for minmax optimization, originally developed for single objective minimization only. The backtracking step of our Lookahead-minmax naturally handles the rotational game dynamics, a property which was identified to be key for enabling gradient ascent descent methods to converge on challenging examples often analyzed in the literature. Moreover, it implicitly handles high variance without using large mini-batches, known to be essential for reaching state of the art performance. Experimental results on MNIST, SVHN, CIFAR-10, and ImageNet demonstrate a clear advantage of combining Lookahead-minmax with Adam or extragradient, in terms of performance and improved stability, for negligible memory and computational cost. Using 30-fold fewer parameters and 16-fold smaller minibatches we outperform the reported performance of the class-dependent BigGAN on CIFAR-10 by obtaining FID of 12.19 without using the class labels, bringing state-of-the-art GAN training within reach of common computational resources.

Ensembles over neural network weights trained from different random initialization, known as deep ensembles, achieve state-of-the-art accuracy and calibration. The recently introduced batch ensembles provide a drop-in replacement that is more parameter efficient. In this paper, we design ensembles not only over weights, but over hyperparameters to improve the state of the art in both settings. For best performance independent of budget, we propose hyper-deep ensembles, a simple procedure that involves a random search over different hyperparameters, themselves stratified across multiple random initializations. Its strong performance highlights the benefit of combining models with both weight and hyperparameter diversity. We further propose a parameter efficient version, hyper-batch ensembles, which builds on the layer structure of batch ensembles and self-tuning networks. The computational and memory costs of our method are notably lower than typical ensembles. On image classification tasks, with MLP, LeNet, ResNet 20 and Wide ResNet 28-10 architectures, we improve upon both deep and batch ensembles.

The dominant term in PAC-Bayes bounds is often the Kullback--Leibler divergence between the posterior and prior. For so-called linear PAC-Bayes risk bounds based on the empirical risk of a fixed posterior kernel, it is possible to minimize the expected value of the bound by choosing the prior to be the expected posterior, which we call the oracle prior on the account that it is distribution dependent. In this work, we show that the bound based on the oracle prior can be suboptimal: In some cases, a stronger bound is obtained by using a data-dependent oracle prior, i.e., a conditional expectation of the posterior, given a subset of the training data that is then excluded from the empirical risk term. While using data to learn a prior is a known heuristic, its essential role in optimal bounds is new. In fact, we show that using data can mean the difference between vacuous and nonvacuous bounds. We apply this new principle in the setting of nonconvex learning, simulating data-dependent oracle priors on MNIST and Fashion MNIST with and without held-out data, and demonstrating new nonvacuous bounds in both cases.

In the following, we assume to have access to a differential equation system Neural Stochastic Differential Equations that describes the dynamics of the target environment model a dynamical environment with neural with low fidelity, e.g. by describing the vector field on nets assigned to their drift and diffusion a reduced dimensionality, by ignoring detailed models terms. The high expressive power of their of some system components, or by avoiding certain nonlinearity comes at the expense of instability dependencies for computational feasibility. We incorporate in the identification of the large set of free the ODE system provided by the domain expert parameters. This paper presents a recipe to into a nonlinear system identification engine, which we improve the prediction accuracy of such models choose to be a Bayesian Neural Stochastic Differential in three steps: i) accounting for epistemic Equation (BNSDE) to cover a large scope of dynamical uncertainty by assuming probabilistic weights, systems, resulting in a hybrid model.

The Gumbel-Max trick is the basis of many relaxed gradient estimators. These estimators are easy to implement and low variance, but the goal of scaling them comprehensively to large combinatorial distributions is still outstanding. Working within the perturbation model framework, we introduce stochastic softmax tricks, which generalize the Gumbel-Softmax trick to combinatorial spaces. Our framework is a unified perspective on existing relaxed estimators for perturbation models, and it contains many novel relaxations. We design structured relaxations for subset selection, spanning trees, arborescences, and others. When compared to less structured baselines, we find that stochastic softmax tricks can be used to train latent variable models that perform better and discover more latent structure.