Estimating causal effects for survival outcomes in the high-dimensional setting is an extremely important topic for many biomedical applications as well as areas of social sciences. We propose a new orthogonal score method for treatment effect estimation and inference that results in asymptotically valid confidence intervals assuming only good estimation properties of the hazard outcome model and the conditional probability of treatment. This guarantee allows us to provide valid inference for the conditional treatment effect under the high-dimensional additive hazards model under considerably more generality than existing approaches. In addition, we develop a new Hazards Difference (HDi), estimator. We showcase that our approach has double-robustness properties in high dimensions: with cross-fitting, the HDi estimate is consistent under a wide variety of treatment assignment models; the HDi estimate is also consistent when the hazards model is misspecified and instead the true data generating mechanism follows a partially linear additive hazards model. We further develop a novel sparsity doubly robust result, where either the outcome or the treatment model can be a fully dense high-dimensional model. We apply our methods to study the treatment effect of radical prostatectomy versus conservative management for prostate cancer patients using the SEER-Medicare Linked Data.

We deal with the \textit{selective classification} problem (supervised-learning problem with a rejection option), where we want to achieve the best performance at a certain level of coverage of the data. We transform the original $m$-class classification problem to $(m+1)$-class where the $(m+1)$-th class represents the model abstaining from making a prediction due to uncertainty. Inspired by portfolio theory, we propose a loss function for the selective classification problem based on the doubling rate of gambling. We show that minimizing this loss function has a natural interpretation as maximizing the return of a \textit{horse race}, where a player aims to balance between betting on an outcome (making a prediction) when confident and reserving one's winnings (abstaining) when not confident. This loss function allows us to train neural networks and characterize the uncertainty of prediction in an end-to-end fashion. In comparison with previous methods, our method requires almost no modification to the model inference algorithm or neural architecture. Experimentally, we show that our method can identify both uncertain and outlier data points, and achieves strong results on SVHN and CIFAR10 at various coverages of the data.

Hierarchical probabilistic models are able to use a large number of parameters to create a model with a high representation power. However, it is well known that increasing the number of parameters also increases the complexity of the model which leads to a bias-variance trade-off. Although it is a classical problem, the bias-variance trade-off between hidden layers and higher-order interactions have not been well studied. In our study, we propose an efficient inference algorithm for the log-linear formulation of the higher-order Boltzmann machine using a combination of Gibbs sampling and annealed importance sampling. We then perform a bias-variance decomposition to study the differences in hidden layers and higher-order interactions. Our results have shown that using hidden layers and higher-order interactions have a comparable error with a similar order of magnitude and using higher-order interactions produce less variance for smaller sample size.

Modeling unknown systems from data is a precursor of system optimization and sequential decision making. In this paper, we focus on learning a Markov model from a single trajectory of states. Suppose that the transition model has a small rank despite of a large state space, meaning that the system admits a low-dimensional latent structure. We show that one can estimate the full transition model accurately using a trajectory of length that is proportional to the total number of states. We propose two maximum likelihood estimation methods: a convex approach with nuclear-norm regularization and a nonconvex approach with rank constraint. We show that both estimators enjoy optimal statistical rates in terms of the Kullback-Leiber divergence and the $\ell_2$ error. For computing the nonconvex estimator, we develop a novel DC (difference of convex function) programming algorithm that starts with the convex M-estimator and then successively refines the solution till convergence. Empirical experiments demonstrate consistent superiority of the nonconvex estimator over the convex one.

One of the most surprising and exciting discoveries in supervising learning was the benefit of overparametrization (i.e. training a very large model) to improving the optimization landscape of a problem, with minimal effect on statistical performance (i.e. generalization). In contrast, unsupervised settings have been under-explored, despite the fact that it has been observed that overparameterization can be helpful as early as Dasgupta & Schulman (2007). In this paper, we perform an exhaustive study of different aspects of overparameterization in unsupervised learning via synthetic and semi-synthetic experiments. We discuss benefits to different metrics of success (held-out log-likelihood, recovering the parameters of the ground-truth model), sensitivity to variations of the training algorithm, and behavior as the amount of overparameterization increases. We find that, when learning using methods such as variational inference, larger models can significantly increase the number of ground truth latent variables recovered.

We present a consensus Monte Carlo algorithm that scales existing Bayesian nonparametric models for clustering and feature allocation to big data. The algorithm is valid for any prior on random subsets such as partitions and latent feature allocation, under essentially any sampling model. Motivated by three case studies, we focus on clustering induced by a Dirichlet process mixture sampling model, inference under an Indian buffet process prior with a binomial sampling model, and with a categorical sampling model. We assess the proposed algorithm with simulation studies and show results for inference with three datasets: an MNIST image dataset, a dataset of pancreatic cancer mutations, and a large set of electronic health records (EHR). Supplementary materials for this article are available online.

Membership inference (MI) attacks exploit a learned model's lack of generalization to infer whether a given sample was in the model's training set. Known MI attacks generally work by casting the attacker's goal as a supervised learning problem, training an attack model from predictions generated by the target model, or by others like it. However, we find that these attacks do not often provide a meaningful basis for confidently inferring training set membership, as the attack models are not well-calibrated. Moreover, these attacks do not significantly outperform a trivial attack that predicts that a point is a member if and only if the model correctly predicts its label. In this work we present well-calibrated MI attacks that allow the attacker to accurately control the minimum confidence with which positive membership inferences are made. Our attacks take advantage of white-box information about the target model and leverage new insights about how overfitting occurs in deep neural networks; namely, we show how a model's idiosyncratic use of features can provide evidence for membership. Experiments on seven real-world datasets show that our attacks support calibration for high-confidence inferences, while outperforming previous MI attacks in terms of accuracy. Finally, we show that our attacks achieve non-trivial advantage on some models with low generalization error, including those trained with small-epsilon-differential privacy; for large-epsilon (epsilon=16, as reported in some industrial settings), the attack performs comparably to unprotected models.

We describe a limitation in the expressiveness of the predictive uncertainty estimate given by mean-field variational inference (MFVI), a popular approximate inference method for Bayesian neural networks. In particular, MFVI fails to give calibrated uncertainty estimates in between separated regions of observations. This can lead to catastrophically overconfident predictions when testing on out-of-distribution data. Avoiding such overconfidence is critical for active learning, Bayesian optimisation and out-of-distribution robustness. We instead find that a classical technique, the linearised Laplace approximation, can handle 'in-between' uncertainty much better for small network architectures.

Discovering cause-effect relationships between variables from observational data is a fundamental challenge in many scientific disciplines. However, in many situations it is desirable to directly estimate the change in causal relationships across two different conditions, e.g., estimating the change in genetic expression across healthy and diseased subjects can help isolate genetic factors behind the disease. This paper focuses on the problem of directly estimating the structural difference between two causal DAGs, having the same topological ordering, given two sets of samples drawn from the individual DAGs. We present an algorithm that can recover the difference-DAG in $O(d \log p)$ samples, where $d$ is related to the number of edges in the difference-DAG. We also show that any method requires at least $\Omega(d \log p/d)$ samples to learn difference DAGs with at most $d$ parents per node. We validate our theoretical results with synthetic experiments and show that our method out-performs the state-of-the-art.

To investigate objects without a describable notion of distance, one can gather ordinal information by asking triplet comparisons of the form "Is object $x$ closer to $y$ or is $x$ closer to $z$?" In order to learn from such data, the objects are typically embedded in a Euclidean space while satisfying as many triplet comparisons as possible. In this paper, we introduce empirical uncertainty estimates for standard embedding algorithms when few noisy triplets are available, using a bootstrap and a Bayesian approach. In particular, simulations show that these estimates are well calibrated and can serve to select embedding parameters or to quantify uncertainty in scientific applications.