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 Uncertainty


How to Train Your Energy-Based Models

arXiv.org Machine Learning

Energy-Based Models (EBMs), also known as non-normalized probabilistic models, specify probability density or mass functions up to an unknown normalizing constant. Unlike most other probabilistic models, EBMs do not place a restriction on the tractability of the normalizing constant, thus are more flexible to parameterize and can model a more expressive family of probability distributions. However, the unknown normalizing constant of EBMs makes training particularly difficult. Our goal is to provide a friendly introduction to modern approaches for EBM training. We start by explaining maximum likelihood training with Markov chain Monte Carlo (MCMC), and proceed to elaborate on MCMC-free approaches, including Score Matching (SM) and Noise Constrastive Estimation (NCE). We highlight theoretical connections among these three approaches, and end with a brief survey on alternative training methods, which are still under active research. Our tutorial is targeted at an audience with basic understanding of generative models who want to apply EBMs or start a research project in this direction.


The Effect of Prior Lipschitz Continuity on the Adversarial Robustness of Bayesian Neural Networks

arXiv.org Machine Learning

It is desirable, and often a necessity, for machine learning models to be robust against adversarial attacks. This is particularly true for Bayesian models, as they are well-suited for safety-critical applications, in which adversarial attacks can have catastrophic outcomes. In this work, we take a deeper look at the adversarial robustness of Bayesian Neural Networks (BNNs). In particular, we consider whether the adversarial robustness of a BNN can be increased by model choices, particularly the Lipschitz continuity induced by the prior. Conducting in-depth analysis on the case of i.i.d., zero-mean Gaussian priors and posteriors approximated via mean-field variational inference, we find evidence that adversarial robustness is indeed sensitive to the prior variance.


Average-Reward Off-Policy Policy Evaluation with Function Approximation

arXiv.org Artificial Intelligence

We consider off-policy policy evaluation with function approximation (FA) in average-reward MDPs, where the goal is to estimate both the reward rate and the differential value function. For this problem, bootstrapping is necessary and, along with off-policy learning and FA, results in the deadly triad (Sutton & Barto, 2018). To address the deadly triad, we propose two novel algorithms, reproducing the celebrated success of Gradient TD algorithms in the average-reward setting. In terms of estimating the differential value function, the algorithms are the first convergent off-policy linear function approximation algorithms. In terms of estimating the reward rate, the algorithms are the first convergent off-policy linear function approximation algorithms that do not require estimating the density ratio. We demonstrate empirically the advantage of the proposed algorithms, as well as their nonlinear variants, over a competitive density-ratio-based approach, in a simple domain as well as challenging robot simulation tasks.


Associated Spatio-Temporal Capsule Network for Gait Recognition

arXiv.org Artificial Intelligence

It is a challenging task to identify a person based on her/his gait patterns. State-of-the-art approaches rely on the analysis of temporal or spatial characteristics of gait, and gait recognition is usually performed on single modality data (such as images, skeleton joint coordinates, or force signals). Evidence has shown that using multi-modality data is more conducive to gait research. Therefore, we here establish an automated learning system, with an associated spatio-temporal capsule network (ASTCapsNet) trained on multi-sensor datasets, to analyze multimodal information for gait recognition. Specifically, we first design a low-level feature extractor and a high-level feature extractor for spatio-temporal feature extraction of gait with a novel recurrent memory unit and a relationship layer. Subsequently, a Bayesian model is employed for the decision-making of class labels. Extensive experiments on several public datasets (normal and abnormal gait) validate the effectiveness of the proposed ASTCapsNet, compared against several state-of-the-art methods.


Drift anticipation with forgetting to improve evolving fuzzy system

arXiv.org Artificial Intelligence

Working with a non-stationary stream of data requires for the analysis system to evolve its model (the parameters as well as the structure) over time. In particular, concept drifts can occur, which makes it necessary to forget knowledge that has become obsolete. However, the forgetting is subjected to the stability-plasticity dilemma, that is, increasing forgetting improve reactivity of adapting to the new data while reducing the robustness of the system. Based on a set of inference rules, Evolving Fuzzy Systems-EFS-have proven to be effective in solving the data stream learning problem. However tackling the stability-plasticity dilemma is still an open question. This paper proposes a coherent method to integrate forgetting in Evolving Fuzzy System, based on the recently introduced notion of concept drift anticipation. The forgetting is applied with two methods: an exponential forgetting of the premise part and a deferred directional forgetting of the conclusion part of EFS to preserve the coherence between both parts. The originality of the approach consists in applying the forgetting only in the anticipation module and in keeping the EFS (called principal system) learned without any forgetting. Then, when a drift is detected in the stream, a selection mechanism is proposed to replace the obsolete parameters of the principal system with more suitable parameters of the anticipation module. An evaluation of the proposed methods is carried out on benchmark online datasets, with a comparison with state-of-the-art online classifiers (Learn++.NSE, PENsemble, pclass) as well as with the original system using different forgetting strategies.


Controlling Synthetic Characters in Simulations: A Case for Cognitive Architectures and Sigma

arXiv.org Artificial Intelligence

Simulations, along with other similar applications like virtual worlds and video games, require computational models of intelligence that generate realistic and credible behavior for the participating synthetic characters. Cognitive architectures, which are models of the fixed structure underlying intelligent behavior in both natural and artificial systems, provide a conceptually valid common basis, as evidenced by the current efforts towards a standard model of the mind, to generate human-like intelligent behavior for these synthetic characters. Sigma is a cognitive architecture and system that strives to combine what has been learned from four decades of independent work on symbolic cognitive architectures, probabilistic graphical models, and more recently neural models, under its graphical architecture hypothesis. Sigma leverages an extended form of factor graphs towards a uniform grand unification of not only traditional cognitive capabilities but also key non-cognitive aspects, creating unique opportunities for the construction of new kinds of cognitive models that possess a Theory-of-Mind and that are perceptual, autonomous, interactive, affective, and adaptive. In this paper, we will introduce Sigma along with its diverse capabilities and then use three distinct proof-of-concept Sigma models to highlight combinations of these capabilities: (1) Distributional reinforcement learning models in; (2) A pair of adaptive and interactive agent models that demonstrate rule-based, probabilistic, and social reasoning; and (3) A knowledge-free exploration model in which an agent leverages only architectural appraisal variables, namely attention and curiosity, to locate an item while building up a map in a Unity environment.


Artificial Intelligence Methods in In-Cabin Use Cases: A Survey

arXiv.org Artificial Intelligence

As interest in autonomous driving increases, efforts are being made to meet requirements for the high-level automation of vehicles. In this context, the functionality inside the vehicle cabin plays a key role in ensuring a safe and pleasant journey for driver and passenger alike. At the same time, recent advances in the field of artificial intelligence (AI) have enabled a whole range of new applications and assistance systems to solve automated problems in the vehicle cabin. This paper presents a thorough survey on existing work that utilizes AI methods for use-cases inside the driving cabin, focusing, in particular, on application scenarios related to (1) driving safety and (2) driving comfort. Results from the surveyed works show that AI technology has a promising future in tackling in-cabin tasks within the autonomous driving aspect.


Identification of Latent Variables From Graphical Model Residuals

arXiv.org Machine Learning

Graph-based causal discovery methods aim to capture conditional independencies consistent with the observed data and differentiate causal relationships from indirect or induced ones. Successful construction of graphical models of data depends on the assumption of causal sufficiency: that is, that all confounding variables are measured. When this assumption is not met, learned graphical structures may become arbitrarily incorrect and effects implied by such models may be wrongly attributed, carry the wrong magnitude, or mis-represent direction of correlation. Wide application of graphical models to increasingly less curated "big data" draws renewed attention to the unobserved confounder problem. We present a novel method that aims to control for the latent space when estimating a DAG by iteratively deriving proxies for the latent space from the residuals of the inferred model. Under mild assumptions, our method improves structural inference of Gaussian graphical models and enhances identifiability of the causal effect. In addition, when the model is being used to predict outcomes, it un-confounds the coefficients on the parents of the outcomes and leads to improved predictive performance when out-of-sample regime is very different from the training data. We show that any improvement of prediction of an outcome is intrinsically capped and cannot rise beyond a certain limit as compared to the confounded model. We extend our methodology beyond GGMs to ordinal variables and nonlinear cases. Our R package provides both PCA and autoencoder implementations of the methodology, suitable for GGMs with some guarantees and for better performance in general cases but without such guarantees.


Provably Efficient Reinforcement Learning with Linear Function Approximation Under Adaptivity Constraints

arXiv.org Machine Learning

We study reinforcement learning (RL) with linear function approximation under the adaptivity constraint. We consider two popular limited adaptivity models: batch learning model and rare policy switch model, and propose two efficient online RL algorithms for linear Markov decision processes. In specific, for the batch learning model, our proposed LSVI-UCB-Batch algorithm achieves an $\tilde O(\sqrt{d^3H^3T} + dHT/B)$ regret, where $d$ is the dimension of the feature mapping, $H$ is the episode length, $T$ is the number of interactions and $B$ is the number of batches. Our result suggests that it suffices to use only $\sqrt{T/dH}$ batches to obtain $\tilde O(\sqrt{d^3H^3T})$ regret. For the rare policy switch model, our proposed LSVI-UCB-RareSwitch algorithm enjoys an $\tilde O(\sqrt{d^3H^3T[1+T/(dH)]^{dH/B}})$ regret, which implies that $dH\log T$ policy switches suffice to obtain the $\tilde O(\sqrt{d^3H^3T})$ regret. Our algorithms achieve the same regret as the LSVI-UCB algorithm (Jin et al., 2019), yet with a substantially smaller amount of adaptivity.


Bayesian Inference of Random Dot Product Graphs via Conic Programming

arXiv.org Machine Learning

We present a convex cone program to infer the latent probability matrix of a random dot product graph (RDPG). The optimization problem maximizes the Bernoulli maximum likelihood function with an added nuclear norm regularization term. The dual problem has a particularly nice form, related to the well-known semidefinite program relaxation of the maxcut problem. Using the primal-dual optimality conditions, we bound the entries and rank of the primal and dual solutions. Furthermore, we bound the optimal objective value and prove asymptotic consistency of the probability estimates of a slightly modified model under mild technical assumptions. Our experiments on synthetic RDPGs not only recover natural clusters, but also reveal the underlying low-dimensional geometry of the original data. We also demonstrate that the method recovers latent structure in the Karate Club Graph and synthetic U.S. Senate vote graphs and is scalable to graphs with up to a few hundred nodes.