Temporal logics over finite traces have recently gained attention due to their use in real-world applications, in particular in business process modelling and planning. In real life, processes contain some degree of uncertainty that is impossible to handle with classical logics. We propose a new probabilistic temporal logic over finite traces based on superposition semantics, where all possible evolutions are possible, until observed. We study the properties of the logic and provide automata-based mechanisms for deriving probabilistic inferences from its formulas. We ground the approach in the context of declarative process modelling, showing how the temporal patterns used in Declare can be lifted to our setting, and discussing how probabilistic inferences can be exploited to provide key offline and runtime reasoning tasks, and how to discover probabilistic Declare patterns from event data by minor adjustments to existing discovery algorithms.

Agents are systems that optimize an objective function in an environment. Together, the goal and the environment induce secondary objectives, incentives. Modeling the agent-environment interaction in graphical models called influence diagrams, we can answer two fundamental questions about an agent's incentives directly from the graph: (1) which nodes is the agent incentivized to observe, and (2) which nodes is the agent incentivized to influence? The answers tell us which information and influence points need extra protection. For example, we may want a classifier for job applications to not use the ethnicity of the candidate, and a reinforcement learning agent not to take direct control of its reward mechanism. Different algorithms and training paradigms can lead to different influence diagrams, so our method can be used to identify algorithms with problematic incentives and help in designing algorithms with better incentives.

This article briefs you about Markov Networks which falls under the family of Undirected Graphical Models (UGM). This article is a follow-up to Bayesian Network, which is a type of Directed Graphical Models. Key Motivation behind these networks is to parameterize the Joint Probability Distribution based on Local Independencies between Random Variables. Generally, Bayesian Network requires to pre-define a directionality to assert an influence of random variable. But there might be cases where interaction between nodes ( or random variables) are symmetric in nature, and we would like to have a model which can represent this symmetricity without directional influence.

Suppose one is faced with the challenge of tissue segmentation in MR images, without annotators at their center to provide labeled training data. One option is to go to another medical center for a trained classifier. Sadly, tissue classifiers do not generalize well across centers due to voxel intensity shifts caused by center-specific acquisition protocols. However, certain aspects of segmentations, such as spatial smoothness, remain relatively consistent and can be learned separately. Here we present a smoothness prior that is fit to segmentations produced at another medical center. This informative prior is presented to an unsupervised Bayesian model. The model clusters the voxel intensities, such that it produces segmentations that are similarly smooth to those of the other medical center. In addition, the unsupervised Bayesian model is extended to a semi-supervised variant, which needs no visual interpretation of clusters into tissues.

We introduce a dynamic generative model, Bayesian allocation model (BAM), which establishes explicit connections between nonnegative tensor factorization (NTF), graphical models of discrete probability distributions and their Bayesian extensions, and the topic models such as the latent Dirichlet allocation. BAM is based on a Poisson process, whose events are marked by using a Bayesian network, where the conditional probability tables of this network are then integrated out analytically. We show that the resulting marginal process turns out to be a Polya urn, an integer valued self-reinforcing process. This urn processes, which we name a Polya-Bayes process, obey certain conditional independence properties that provide further insight about the nature of NTF. These insights also let us develop space efficient simulation algorithms that respect the potential sparsity of data: we propose a class of sequential importance sampling algorithms for computing NTF and approximating their marginal likelihood, which would be useful for model selection. The resulting methods can also be viewed as a model scoring method for topic models and discrete Bayesian networks with hidden variables. The new algorithms have favourable properties in the sparse data regime when contrasted with variational algorithms that become more accurate when the total sum of the elements of the observed tensor goes to infinity. We illustrate the performance on several examples and numerically study the behaviour of the algorithms for various data regimes.

In this work, a deep learning-based method for log-likelihood ratio (LLR) lossy compression and quantization is proposed, with emphasis on a single-input single-output uncorrelated fading communication setting. A deep autoencoder network is trained to compress, quantize and reconstruct the bit log-likelihood ratios corresponding to a single transmitted symbol. Specifically, the encoder maps to a latent space with dimension equal to the number of sufficient statistics required to recover the inputs - equal to three in this case - while the decoder aims to reconstruct a noisy version of the latent representation with the purpose of modeling quantization effects in a differentiable way. Simulation results show that, when applied to a standard rate-1/2 low-density parity-check (LDPC) code, a finite precision compression factor of nearly three times is achieved when storing an entire codeword, with an incurred loss of performance lower than 0.1 dB compared to straightforward scalar quantization of the log-likelihood ratios.

While MCMC methods have become a main work-horse for Bayesian inference, scaling them to large distributed datasets is still a challenge. Embarrassingly parallel MCMC strategies take a divide-and-conquer stance to achieve this by writing the target posterior as a product of subposteriors, running MCMC for each of them in parallel and subsequently combining the results. The challenge then lies in devising efficient aggregation strategies. Current strategies trade-off between approximation quality, and costs of communication and computation. In this work, we introduce a novel method that addresses these issues simultaneously. Our key insight is to introduce a deep invertible transformation to approximate each of the subposteriors. These approximations can be made accurate even for complex distributions and serve as intermediate representations, keeping the total communication cost limited. Moreover, they enable us to sample from the product of the subposteriors using an efficient and stable importance sampling scheme. We demonstrate the approach outperforms available state-of-the-art methods in a range of challenging scenarios, including high-dimensional and heterogeneous subposteriors.

Our approach leverages the well known Burer-Monteiro factorisation strategy from large scale optimisation, in the context of low rank estimation. Moreover, our Burer-Monteiro factors are shown to lie on a Stiefel manifold. We propose a new generalized Bayesian estimator for this problem and prove novel prediction bounds for clustering. We also devise a componentwise Langevin sampler on the Stiefel manifold to compute this estimator.

We consider multi-task regression models where observations are assumed to be a linear combination of several latent node and weight functions, all drawn from Gaussian process priors that allow nonzero covariance between grouped latent functions. Motivated by the problem of developing scalable methods for distributed solar forecasting, we exploit sparse covariance structures where latent functions are assumed to be conditionally independent given a group-pivot latent function. We exploit properties of multivariate Gaussians to construct sparse Cholesky factors directly, rather than obtaining them through iterative routines, and by doing so achieve significantly improved time and memory complexity including prediction complexity that is linear in the number of grouped functions. We test our approach on large multi-task datasets and find that sparse specifications achieve the same or better accuracy than non-sparse counterparts in less time, and improve on benchmark model accuracy.

We propose a novel approach for posterior sampling with intractable likelihoods. This is an increasingly important problem in scientific applications where models are implemented as sophisticated computer simulations. As a result, tractable densities are not available, which forces practitioners to rely on approximations during inference. We address the intractability of densities by training a parameterized classifier whose output is used to approximate likelihood ratios between arbitrary model parameters. In turn, we are able to draw posterior samples by plugging this approximator into common Markov chain Monte Carlo samplers such as Metropolis-Hastings and Hamiltonian Monte Carlo. We demonstrate the proposed technique by fitting the generating parameters of implicit models, ranging from a linear probabilistic model to settings in high energy physics with high-dimensional observations. Finally, we discuss several diagnostics to assess the quality of the posterior.