We study the parameter estimation problem in mixture models with observational nonidentifiability: the full model (also containing hidden variables) is identifiable, but the marginal (observed) model is not. Hence global maxima of the marginal likelihood are (infinitely) degenerate and predictions of the marginal likelihood are not unique. We show how to generalize the marginal likelihood by introducing an effective temperature, and making it similar to the free energy. This generalization resolves the observational nonidentifiability, since its maximization leads to unique results that are better than a random selection of one degenerate maximum of the marginal likelihood or the averaging over many such maxima. The generalized likelihood inherits many features from the usual likelihood, e.g. it holds the conditionality principle, and its local maximum can be searched for via suitably modified expectation-maximization method. The maximization of the generalized likelihood relates to entropy optimization.

Neural networks utilize the softmax as a building block in classification tasks, which contains an overconfidence problem and lacks an uncertainty representation ability. As a Bayesian alternative to the softmax, we consider a random variable of a categorical probability over class labels. In this framework, the prior distribution explicitly models the presumed noise inherent in the observed label, which provides consistent gains in generalization performance in multiple challenging tasks. The proposed method inherits advantages of Bayesian approaches that achieve better uncertainty estimation and model calibration. Our method can be implemented as a plug-and-play loss function with negligible computational overhead compared to the softmax with the cross-entropy loss function.

Despite substantial progress in signal source separation, results for richly structured data continue to contain perceptible artifacts. In contrast, recent deep generative models can produce authentic samples in a variety of domains that are indistinguishable from samples of the data distribution. This paper introduces a Bayesian approach to source separation that uses generative models as priors over the components of a mixture of sources, and Langevin dynamics to sample from the posterior distribution of sources given a mixture. This decouples the source separation problem from generative modeling, enabling us to directly use cutting-edge generative models as priors. The method achieves state-of-the-art performance for MNIST digit separation. We introduce new methodology for evaluating separation quality on richer datasets, providing quantitative evaluation of separation results on CIFAR-10. We also provide qualitative results on LSUN.

[Abridged] Although galaxies are found to follow a tight relation between their star formation rate and stellar mass, they are expected to exhibit complex star formation histories (SFH), with short-term fluctuations. The goal of this pilot study is to present a method that will identify galaxies that are undergoing a strong variation of star formation activity in the last tens to hundreds Myr. In other words, the proposed method will determine whether a variation in the last few hundreds of Myr of the SFH is needed to properly model the SED rather than a smooth normal SFH. To do so, we analyze a sample of COSMOS galaxies using high signal-to-noise ratio broad band photometry. We apply Approximate Bayesian Computation, a state-of-the-art statistical method to perform model choice, associated to machine learning algorithms to provide the probability that a flexible SFH is preferred based on the observed flux density ratios of galaxies. We present the method and test it on a sample of simulated SEDs. The input information fed to the algorithm is a set of broadband UV to NIR (rest-frame) flux ratios for each galaxy. The method has an error rate of 21% in recovering the right SFH and is sensitive to SFR variations larger than 1 dex. A more traditional SED fitting method using CIGALE is tested to achieve the same goal, based on fits comparisons through Bayesian Information Criterion but the best error rate obtained is higher, 28%. We apply our new method to the COSMOS galaxies sample. The stellar mass distribution of galaxies with a strong to decisive evidence against the smooth delayed-$\tau$ SFH peaks at lower M* compared to galaxies where the smooth delayed-$\tau$ SFH is preferred. We discuss the fact that this result does not come from any bias due to our training. Finally, we argue that flexible SFHs are needed to be able to cover that largest SFR-M* parameter space possible.

In this paper, a Neural network is derived from first principles, assuming only that each layer begins with a linear dimension-reducing transformation. The approach appeals to the principle of Maximum Entropy (MaxEnt) to find the posterior distribution of the input data of each layer, conditioned on the layer output variables. This posterior has a well-defined mean, the conditional mean estimator, that is calculated using a type of neural network with theoretically-derived activation functions similar to sigmoid, softplus, and relu. This implicitly provides a theoretical justification for their use. A theorem that finds the conditional distribution and conditional mean estimator under the MaxEnt prior is proposed, unifying results for special cases. Combining layers results in an auto-encoder with conventional feed-forward analysis network and a type of linear Bayesian belief network in the reconstruction path.

The notions of distance and similarity play a key role in many machine learning approaches, and artificial intelligence (AI) in general, since they can serve as an organizing principle by which individuals classify objects, form concepts and make generalizations. While distance functions for propositional representations have been thoroughly studied, work on distance functions for structured representations, such as graphs, frames or logical clauses, has been carried out in different communities and is much less understood. Specifically, a significant amount of work that requires the use of a distance or similarity function for structured representations of data usually employs ad-hoc functions for specific applications. Therefore, the goal of this paper is to provide an overview of this work to identify connections between the work carried out in different areas and point out directions for future work.

Robots are required to not only learn spatial concepts autonomously but also utilize such knowledge for various tasks in a domestic environment. Spatial concept represents a multimodal place category acquired from the robot's spatial experience including vision, speech-language, and self-position. The aim of this study is to enable a mobile robot to perform navigational tasks with human speech instructions, such as `Go to the kitchen', via probabilistic inference on a Bayesian generative model using spatial concepts. Specifically, path planning was formalized as the maximization of probabilistic distribution on the path-trajectory under speech instruction, based on a control-as-inference framework. Furthermore, we described the relationship between probabilistic inference based on the Bayesian generative model and control problem including reinforcement learning. We demonstrated path planning based on human instruction using acquired spatial concepts to verify the usefulness of the proposed approach in the simulator and in real environments. Experimentally, places instructed by the user's speech commands showed high probability values, and the trajectory toward the target place was correctly estimated. Our approach, based on probabilistic inference concerning decision-making, can lead to further improvement in robot autonomy.

A Relational Markov Decision Process (RMDP) is a first-order representation to express all instances of a single probabilistic planning domain with possibly unbounded number of objects. Early work in RMDPs outputs generalized (instance-independent) first-order policies or value functions as a means to solve all instances of a domain at once. Unfortunately, this line of work met with limited success due to inherent limitations of the representation space used in such policies or value functions. Can neural models provide the missing link by easily representing more complex generalized policies, thus making them effective on all instances of a given domain? We present the first neural approach for solving RMDPs, expressed in the probabilistic planning language of RDDL. Our solution first converts an RDDL instance into a ground DBN. We then extract a graph structure from the DBN. We train a relational neural model that computes an embedding for each node in the graph and also scores each ground action as a function over the first-order action variable and object embeddings on which the action is applied. In essence, this represents a neural generalized policy for the whole domain. Given a new test problem of the same domain, we can compute all node embeddings using trained parameters and score each ground action to choose the best action using a single forward pass without any retraining. Our experiments on nine RDDL domains from IPPC demonstrate that neural generalized policies are significantly better than random and sometimes even more effective than training a state-of-the-art deep reactive policy from scratch.

Sum-product networks (SPNs) are flexible density estimators and have received significant attention due to their attractive inference properties. While parameter learning in SPNs is well developed, structure learning leaves something to be desired: even though there is a plethora of SPN structure learners, most of them are somewhat ad-hoc, and based on intuition rather than a clear learning principle. In this paper, we introduce a well-principled Bayesian framework for SPN structure learning. The first is rather unproblematic and akin to neural network architecture validation. The second characterizes the effective structure of the SPN and needs to respect the usual structural constraints in SPN, i.e., completeness and decomposability.

Policy evaluation is a key process in Reinforcement Learning (RL). It assesses a given policy by estimating the corresponding value function. When using parameterized value functions, common approaches minimize the sum of squared Bellman temporal-difference errors and receive a point-estimate for the parameters. Kalman-based and Gaussian-processes based frameworks were suggested to evaluate the policy by treating the value as a random variable. These frameworks can learn uncertainties over the value parameters and exploit them for policy exploration. When adopting these frameworks to solve deep RL tasks, several limitations are revealed: excessive computations in each optimization step, difficulty with handling batches of samples which slows training and the effect of memory in stochastic environments which prevents off-policy learning. In this work, we discuss these limitations and propose to overcome them by an alternative general framework, based on the extended Kalman filter. We devise an optimization method, called Kalman Optimization for Value Approximation (KOVA) that can be incorporated as a policy evaluation component in policy optimization algorithms. KOVA minimizes a regularized objective function that concerns both parameter and noisy return uncertainties. We analyze the properties of KOVA and present its performance on deep RL control tasks.