Our goal is to recover time-delayed latent causal variables and identify their relations from measured temporal data. Estimating causally-related latent variables from observations is particularly challenging as the latent variables are not uniquely recoverable in the most general case. In this work, we consider both a nonparametric, nonstationary setting and a parametric setting for the latent processes and propose two provable conditions under which temporally causal latent processes can be identified from their nonlinear mixtures. We propose LEAP, a theoretically-grounded framework that extends Variational AutoEncoders (VAEs) by enforcing our conditions through proper constraints in causal process prior. Experimental results on various datasets demonstrate that temporally causal latent processes are reliably identified from observed variables under different dependency structures and that our approach considerably outperforms baselines that do not properly leverage history or nonstationarity information. This demonstrates that using temporal information to learn latent processes from their invertible nonlinear mixtures in an unsupervised manner, for which we believe our work is one of the first, seems promising even without sparsity or minimality assumptions.
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Anomaly detection among a large number of processes arises in many applications ranging from dynamic spectrum access to cybersecurity. In such problems one can often obtain noisy observations aggregated from a chosen subset of processes that conforms to a tree structure. The distribution of these observations, based on which the presence of anomalies is detected, may be only partially known. This gives rise to the need for a search strategy designed to account for both the sample complexity and the detection accuracy, as well as cope with statistical models that are known only up to some missing parameters. In this work we propose a sequential search strategy using two variations of the Generalized Local Likelihood Ratio statistic. Our proposed Hierarchical Dynamic Search (HDS) strategy is shown to be order-optimal with respect to the size of the search space and asymptotically optimal with respect to the detection accuracy. An explicit upper bound on the error probability of HDS is established for the finite sample regime. Extensive experiments are conducted, demonstrating the performance gains of HDS over existing methods.
Applications of Reinforcement Learning (RL), in which agents learn to make a sequence of decisions despite lacking complete information about the latent states of the controlled system, that is, they act under partial observability of the states, are ubiquitous. Partially observable RL can be notoriously difficult -- well-known information-theoretic results show that learning partially observable Markov decision processes (POMDPs) requires an exponential number of samples in the worst case. Yet, this does not rule out the existence of large subclasses of POMDPs over which learning is tractable. In this paper we identify such a subclass, which we call weakly revealing POMDPs. This family rules out the pathological instances of POMDPs where observations are uninformative to a degree that makes learning hard. We prove that for weakly revealing POMDPs, a simple algorithm combining optimism and Maximum Likelihood Estimation (MLE) is sufficient to guarantee polynomial sample complexity. To the best of our knowledge, this is the first provably sample-efficient result for learning from interactions in overcomplete POMDPs, where the number of latent states can be larger than the number of observations.
We present a data-efficient framework for solving sequential decision-making problems which exploits the combination of reinforcement learning (RL) and latent variable generative models. The framework, called GenRL, trains deep policies by introducing an action latent variable such that the feed-forward policy search can be divided into two parts: (i) training a sub-policy that outputs a distribution over the action latent variable given a state of the system, and (ii) unsupervised training of a generative model that outputs a sequence of motor actions conditioned on the latent action variable. GenRL enables safe exploration and alleviates the data-inefficiency problem as it exploits prior knowledge about valid sequences of motor actions. Moreover, we provide a set of measures for evaluation of generative models such that we are able to predict the performance of the RL policy training prior to the actual training on a physical robot. We experimentally determine the characteristics of generative models that have most influence on the performance of the final policy training on two robotics tasks: shooting a hockey puck and throwing a basketball. Furthermore, we empirically demonstrate that GenRL is the only method which can safely and efficiently solve the robotics tasks compared to two state-of-the-art RL methods.
We consider M-estimation problems, where the target value is determined using a minimizer of an expected functional of a Levy process. With discrete observations from the Levy process, we can produce a "quasi-path" by shuffling increments of the Levy process, we call it a quasi-process. Under a suitable sampling scheme, a quasi-process can converge weakly to the true process according to the properties of the stationary and independent increments. Using this resampling technique, we can estimate objective functionals similar to those estimated using the Monte Carlo simulations, and it is available as a contrast function. The M-estimator based on these quasi-processes can be consistent and asymptotically normal.
When cast into the Deep Reinforcement Learning framework, many robotics tasks require solving a long horizon and sparse reward problem, where learning algorithms struggle. In such context, Imitation Learning (IL) can be a powerful approach to bootstrap the learning process. However, most IL methods require several expert demonstrations which can be prohibitively difficult to acquire. Only a handful of IL algorithms have shown efficiency in the context of an extreme low expert data regime where a single expert demonstration is available. In this paper, we present a novel algorithm designed to imitate complex robotic tasks from the states of an expert trajectory. Based on a sequential inductive bias, our method divides the complex task into smaller skills. The skills are learned into a goal-conditioned policy that is able to solve each skill individually and chain skills to solve the entire task. We show that our method imitates a non-holonomic navigation task and scales to a complex simulated robotic manipulation task with very high sample efficiency.
Reinforcement learning (RL) has shown great success in solving many challenging tasks via use of deep neural networks. Although using deep learning for RL brings immense representational power, it also causes a well-known sample-inefficiency problem. This means that the algorithms are data-hungry and require millions of training samples to converge to an adequate policy. One way to combat this issue is to use action advising in a teacher-student framework, where a knowledgeable teacher provides action advice to help the student. This work considers how to better leverage uncertainties about when a student should ask for advice and if the student can model the teacher to ask for less advice. The student could decide to ask for advice when it is uncertain or when both it and its model of the teacher are uncertain. In addition to this investigation, this paper introduces a new method to compute uncertainty for a deep RL agent using a secondary neural network. Our empirical results show that using dual uncertainties to drive advice collection and reuse may improve learning performance across several Atari games.
Models for dependent data are distinguished by their targets of inference. Marginal models are useful when interest lies in quantifying associations averaged across a population of clusters. When the functional form of a covariate-outcome association is unknown, flexible regression methods are needed to allow for potentially non-linear relationships. We propose a novel marginal additive model (MAM) for modelling cluster-correlated data with non-linear population-averaged associations. The proposed MAM is a unified framework for estimation and uncertainty quantification of a marginal mean model, combined with inference for between-cluster variability and cluster-specific prediction. We propose a fitting algorithm that enables efficient computation of standard errors and corrects for estimation of penalty terms. We demonstrate the proposed methods in simulations and in application to (i) a longitudinal study of beaver foraging behaviour, and (ii) a spatial analysis of Loaloa infection in West Africa. R code for implementing the proposed methodology is available at //github.com/awstringer1/mam.
Learning disentanglement aims at finding a low dimensional representation which consists of multiple explanatory and generative factors of the observational data. The framework of variational autoencoder (VAE) is commonly used to disentangle independent factors from observations. However, in real scenarios, factors with semantics are not necessarily independent. Instead, there might be an underlying causal structure which renders these factors dependent. We thus propose a new VAE based framework named CausalVAE, which includes a Causal Layer to transform independent exogenous factors into causal endogenous ones that correspond to causally related concepts in data. We further analyze the model identifiabitily, showing that the proposed model learned from observations recovers the true one up to a certain degree. Experiments are conducted on various datasets, including synthetic and real word benchmark CelebA. Results show that the causal representations learned by CausalVAE are semantically interpretable, and their causal relationship as a Directed Acyclic Graph (DAG) is identified with good accuracy. Furthermore, we demonstrate that the proposed CausalVAE model is able to generate counterfactual data through "do-operation" to the causal factors.
This paper focuses on the expected difference in borrower's repayment when there is a change in the lender's credit decisions. Classical estimators overlook the confounding effects and hence the estimation error can be magnificent. As such, we propose another approach to construct the estimators such that the error can be greatly reduced. The proposed estimators are shown to be unbiased, consistent, and robust through a combination of theoretical analysis and numerical testing. Moreover, we compare the power of estimating the causal quantities between the classical estimators and the proposed estimators. The comparison is tested across a wide range of models, including linear regression models, tree-based models, and neural network-based models, under different simulated datasets that exhibit different levels of causality, different degrees of nonlinearity, and different distributional properties. Most importantly, we apply our approaches to a large observational dataset provided by a global technology firm that operates in both the e-commerce and the lending business. We find that the relative reduction of estimation error is strikingly substantial if the causal effects are accounted for correctly.
We present a new method to learn video representations from large-scale unlabeled video data. Ideally, this representation will be generic and transferable, directly usable for new tasks such as action recognition and zero or few-shot learning. We formulate unsupervised representation learning as a multi-modal, multi-task learning problem, where the representations are shared across different modalities via distillation. Further, we introduce the concept of loss function evolution by using an evolutionary search algorithm to automatically find optimal combination of loss functions capturing many (self-supervised) tasks and modalities. Thirdly, we propose an unsupervised representation evaluation metric using distribution matching to a large unlabeled dataset as a prior constraint, based on Zipf's law. This unsupervised constraint, which is not guided by any labeling, produces similar results to weakly-supervised, task-specific ones. The proposed unsupervised representation learning results in a single RGB network and outperforms previous methods. Notably, it is also more effective than several label-based methods (e.g., ImageNet), with the exception of large, fully labeled video datasets.
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