We propose a flexible ensemble classification framework, Random Subspace Ensemble (RaSE), for sparse classification. In the RaSE algorithm, we aggregate many weak learners, where each weak learner is a base classifier trained in a subspace optimally selected from a collection of random subspaces. To conduct subspace selection, we propose a new criterion, ratio information criterion (RIC), based on weighted Kullback-Leibler divergence. The theoretical analysis includes the risk and Monte-Carlo variance of RaSE classifier, establishing the screening consistency and weak consistency of RIC, and providing an upper bound for the misclassification rate of RaSE classifier. In addition, we show that in a high-dimensional framework, the number of random subspaces needs to be very large to guarantee that a subspace covering signals is selected. Therefore, we propose an iterative version of RaSE algorithm and prove that under some specific conditions, a smaller number of generated random subspaces are needed to find a desirable subspace through iteration. An array of simulations under various models and real-data applications demonstrate the effectiveness and robustness of the RaSE classifier and its iterative version in terms of low misclassification rate and accurate feature ranking. The RaSE algorithm is implemented in the R package RaSEn on CRAN.

It has been hypothesized that label smoothing can reduce overfitting and improve generalization, and current empirical evidence seems to corroborate these effects. However, there is a lack of mathematical understanding of when and why such empirical improvements occur. In this paper, as a step towards understanding why label smoothing is effective, we propose a theoretical framework to show how label smoothing provides in controlling the generalization loss. In particular, we show that this benefit can be precisely formulated and identified in the label noise setting, where the training is partially mislabeled. Our theory also predicts the existence of an optimal label smoothing point, a single value for the label smoothing hyperparameter that minimizes generalization loss. Extensive experiments are done to confirm the predictions of our theory. We believe that our findings will help both theoreticians and practitioners understand label smoothing, and better apply them to real-world datasets.

The standard approach to fitting an autoregressive spike train model is to maximize the likelihood for one-step prediction. This maximum likelihood estimation (MLE) often leads to models that perform poorly when generating samples recursively for more than one time step. Moreover, the generated spike trains can fail to capture important features of the data and even show diverging firing rates. To alleviate this, we propose to directly minimize the divergence between neural recorded and model generated spike trains using spike train kernels. We develop a method that stochastically optimizes the maximum mean discrepancy induced by the kernel. Experiments performed on both real and synthetic neural data validate the proposed approach, showing that it leads to well-behaving models. Using different combinations of spike train kernels, we show that we can control the trade-off between different features which is critical for dealing with model-mismatch.

Missing data can be informative. Ignoring this information can lead to misleading conclusions when the data model does not allow information to be extracted from the missing data. We propose a co-clustering model, based on the Latent Block Model, that aims to take advantage of this nonignorable nonresponses, also known as Missing Not At Random data (MNAR). A variational expectation-maximization algorithm is derived to perform inference and a model selection criterion is presented. We assess the proposed approach on a simulation study, before using our model on the voting records from the lower house of the French Parliament, where our analysis brings out relevant groups of MPs and texts, together with a sensible interpretation of the behavior of non-voters.

Despite recent advances, goal-directed generation of structured discrete data remains challenging. For problems such as program synthesis (generating source code) and materials design (generating molecules), finding examples which satisfy desired constraints or exhibit desired properties is difficult. In practice, expensive heuristic search or reinforcement learning algorithms are often employed. In this paper we investigate the use of conditional generative models which directly attack this inverse problem, by modeling the distribution of discrete structures given properties of interest. Unfortunately, maximum likelihood training of such models often fails with the samples from the generative model inadequately respecting the input properties. To address this, we introduce a novel approach to directly optimize a reinforcement learning objective, maximizing an expected reward. We avoid high-variance score-function estimators that would otherwise be required by sampling from an approximation to the normalized rewards, allowing simple Monte Carlo estimation of model gradients. We test our methodology on two tasks: generating molecules with user-defined properties, and identifying short python expressions which evaluate to a given target value. In both cases we find improvements over maximum likelihood estimation and other baselines.

Recent research has seen several advances relevant to black-box VI, but the current state of automatic posterior inference is unclear. One such advance is the use of normalizing flows to define flexible posterior densities for deep latent variable models. Another direction is the integration of Monte-Carlo methods to serve two purposes; first, to obtain tighter variational objectives for optimization, and second, to define enriched variational families through sampling. However, both flows and variational Monte-Carlo methods remain relatively unexplored for black-box VI. Moreover, on a pragmatic front, there are several optimization considerations like step-size scheme, parameter initialization, and choice of gradient estimators, for which there are no clear guidance in the existing literature. In this paper, we postulate that black-box VI is best addressed through a careful combination of numerous algorithmic components. We evaluate components relating to optimization, flows, and Monte-Carlo methods on a benchmark of 30 models from the Stan model library. The combination of these algorithmic components significantly advances the state-of-the-art "out of the box" variational inference.

Learning graphical structure based on Directed Acyclic Graphs (DAGs) is a challenging problem, partly owing to the large search space of possible graphs. A recent line of work formulates the structure learning problem as a continuous constrained optimization task using the least squares objective and an algebraic characterization of DAGs. However, the formulation requires a hard DAG constraint and may lead to optimization difficulties. In this paper, we study the asymptotic role of the sparsity and DAG constraints for learning DAG models in the linear Gaussian and non-Gaussian cases, and investigate their usefulness in the finite sample regime. Based on the theoretical results, we formulate a likelihood-based score function, and show that one only has to apply soft sparsity and DAG constraints to learn a DAG equivalent to the ground truth DAG. This leads to an unconstrained optimization problem that is much easier to solve. Using gradient-based optimization and GPU acceleration, our procedure can easily handle thousands of nodes while retaining a high accuracy. Extensive experiments validate the effectiveness of our proposed method and show that the DAG-penalized likelihood objective is indeed favorable over the least squares one with the hard DAG constraint.

Existing methods for estimating uncertainty in deep learning tend to require multiple forward passes, making them unsuitable for applications where computational resources are limited. To solve this, we perform probabilistic reasoning over the depth of neural networks. Different depths correspond to subnetworks which share weights and whose predictions are combined via marginalisation, yielding model uncertainty. By exploiting the sequential structure of feed-forward networks, we are able to both evaluate our training objective and make predictions with a single forward pass. We validate our approach on real-world regression and image classification tasks. Our approach provides uncertainty calibration, robustness to dataset shift, and accuracies competitive with more computationally expensive baselines.

In spite of several claims stating that some models are more interpretable than others -- e.g., "linear models are more interpretable than deep neural networks" -- we still lack a principled notion of interpretability to formally compare among different classes of models. We make a step towards such a notion by studying whether folklore interpretability claims have a correlate in terms of computational complexity theory. We focus on local post-hoc explainability queries that, intuitively, attempt to answer why individual inputs are classified in a certain way by a given model. In a nutshell, we say that a class $\mathcal{C}_1$ of models is more interpretable than another class $\mathcal{C}_2$, if the computational complexity of answering post-hoc queries for models in $\mathcal{C}_2$ is higher than for those in $\mathcal{C}_1$. We prove that this notion provides a good theoretical counterpart to current beliefs on the interpretability of models; in particular, we show that under our definition and assuming standard complexity-theoretical assumptions (such as P$\neq$NP), both linear and tree-based models are strictly more interpretable than neural networks. Our complexity analysis, however, does not provide a clear-cut difference between linear and tree-based models, as we obtain different results depending on the particular post-hoc explanations considered. Finally, by applying a finer complexity analysis based on parameterized complexity, we are able to prove a theoretical result suggesting that shallow neural networks are more interpretable than deeper ones.

Undirected graphical models are compact representations of joint probability distributions over random variables. To solve inference tasks of interest, graphical models of arbitrary topology can be trained using empirical risk minimization. However, to solve inference tasks that were not seen during training, these models (EGMs) often need to be re-trained. Instead, we propose an inference-agnostic adversarial training framework which produces an infinitely-large ensemble of graphical models (AGMs). The ensemble is optimized to generate data within the GAN framework, and inference is performed using a finite subset of these models. AGMs perform comparably with EGMs on inference tasks that the latter were specifically optimized for. Most importantly, AGMs show significantly better generalization to unseen inference tasks compared to EGMs, as well as deep neural architectures like GibbsNet and VAEAC which allow arbitrary conditioning. Finally, AGMs allow fast data sampling, competitive with Gibbs sampling from EGMs.