Neural Information Processing Systems http://nips.cc/

This paper provides the first formalization of self-interested planning in multiagent settings using expectation-maximization (EM). Our formalization in the context of infinite-horizon and finitely-nested interactive POMDPs (I-POMDP) is distinct from EM formulations for POMDPs and cooperative multiagent planning frameworks. We exploit the graphical model structure specific to I-POMDPs, and present a new approach based on block-coordinate descent for further speed up. Forward filtering-backward sampling - a combination of exact filtering with sampling - is explored to exploit problem structure.

Computing a {\em maximum a posteriori} (MAP) assignment in graphical models is a crucial inference problem for many practical applications. Several provably convergent approaches have been successfully developed using linear programming (LP) relaxation of the MAP problem. We present an alternative approach, which transforms the MAP problem into that of inference in a finite mixture of simple Bayes nets. We then derive the Expectation Maximization (EM) algorithm for this mixture that also monotonically increases a lower bound on the MAP assignment until convergence. The update equations for the EM algorithm are remarkably simple, both conceptually and computationally, and can be implemented using a graph-based message passing paradigm similar to max-product computation.

Recently, diffusion models have been successfully applied to improving adversarial robustness of image classifiers by purifying the adversarial noises or generating realistic data for adversarial training. However, the diffusion-based purification can be evaded by stronger adaptive attacks while adversarial training does not perform well under unseen threats, exhibiting inevitable limitations of these methods. To better harness the expressive power of diffusion models, in this paper we propose Robust Diffusion Classifier (RDC), a generative classifier that is constructed from a pre-trained diffusion model to be adversarially robust. Our method first maximizes the data likelihood of a given input and then predicts the class probabilities of the optimized input using the conditional likelihood of the diffusion model through Bayes' theorem. Since our method does not require training on particular adversarial attacks, we demonstrate that it is more generalizable to defend against multiple unseen threats. In particular, RDC achieves $73.24\%$ robust accuracy against $\ell_\infty$ norm-bounded perturbations with $\epsilon_\infty=8/255$ on CIFAR-10, surpassing the previous state-of-the-art adversarial training models by $+2.34\%$. The findings highlight the potential of generative classifiers by employing diffusion models for adversarial robustness compared with the commonly studied discriminative classifiers.

Some of the published Normalizing flows are deep generative models approaches assume a dimensionality-reducing (DGM) that represent the probability distribution map to be known and available a priori [12, 13]. of high-dimensional data sets as a change of variables Other works use compositions of manifold learning of a multivariate Gaussian [1, 2]. Using the inverse models and normalizing flows that are trained simultaneously, of this transformation, normalizing flows can e.g., the M-Flow [6], Noisy Injective compute the probability density functions (PDFs) Flows [14], piecewise injective flows called Trumpets explicitly, thus enabling training via the statistically [15], and neural manifold ordinary differential consistent and asymptotically efficient [3] likelihood equations [16].

This paper considers a sensitivity analysis in Hidden Markov Models with continuous state and observation spaces. We propose an Infinitesimal Perturbation Analysis (IPA) on the filtering distribution with respect to some parameters of the model. We describe a methodology for using any algorithm that estimates the filtering density, such as Sequential Monte Carlo methods, to design an algorithm that estimates its gradient. The resulting IPA estimator is proven to be asymptotically unbiased, consistent and has computational complexity linear in the number of particles. We consider an application of this analysis to the problem of identifying unknown parameters of the model given a sequence of observations.

Computing a {\em maximum a posteriori} (MAP) assignment in graphical models is a crucial inference problem for many practical applications. Several provably convergent approaches have been successfully developed using linear programming (LP) relaxation of the MAP problem. We present an alternative approach, which transforms the MAP problem into that of inference in a finite mixture of simple Bayes nets. We then derive the Expectation Maximization (EM) algorithm for this mixture that also monotonically increases a lower bound on the MAP assignment until convergence. The update equations for the EM algorithm are remarkably simple, both conceptually and computationally, and can be implemented using a graph-based message passing paradigm similar to max-product computation.

This paper considers a sensitivity analysis in Hidden Markov Models with continuous state and observation spaces. We propose an Infinitesimal Perturbation Analysis (IPA) on the filtering distribution with respect to some parameters of the model. We describe a methodology for using any algorithm that estimates the filtering density, such as Sequential Monte Carlo methods, to design an algorithm that estimates its gradient. The resulting IPA estimator is proven to be asymptotically unbiased, consistent and has computational complexity linear in the number of particles. We consider an application of this analysis to the problem of identifying unknown parameters of the model given a sequence of observations.

Iterative Proportional Fitting (IPF), combined with EM, is commonly used as an algorithm for likelihood maximization in undirected graphical models. In this paper, we present two iterative algorithms that generalize upon IPF. The first one is for likelihood maximization in discrete chain factor graphs, which we define as a wide class of discrete variable models including undirected graphical models and Bayesian networks, but also chain graphs and sigmoid belief networks. The second one is for conditional likelihood maximization in standard undirected models and Bayesian networks. In both algorithms, the iteration steps are expressed in closed form. Numerical simulations show that the algorithms are competitive with state of the art methods.

This paper considers a sensitivity analysis in Hidden Markov Models with continuous state and observation spaces. We propose an Infinitesimal Perturbation Analysis (IPA) on the filtering distribution with respect to some parameters of the model. We describe a methodology for using any algorithm that estimates the filtering density, such as Sequential Monte Carlo methods, to design an algorithm that estimates its gradient. The resulting IPA estimator is proven to be asymptotically unbiased, consistent and has computational complexity linear in the number of particles. We consider an application of this analysis to the problem of identifying unknown parameters of the model given a sequence of observations. We derive an IPA estimator for the gradient of the log-likelihood, which may be used in a gradient method for the purpose of likelihood maximization. We illustrate the method with several numerical experiments.