Word meaning changes over time, depending on linguistic and extra-linguistic factors. Associating a word's correct meaning in its historical context is a critical challenge in diachronic research, and is relevant to a range of NLP tasks, including information retrieval and semantic search in historical texts. Bayesian models for semantic change have emerged as a powerful tool to address this challenge, providing explicit and interpretable representations of semantic change phenomena. However, while corpora typically come with rich metadata, existing models are limited by their inability to exploit contextual information (such as text genre) beyond the document time-stamp. This is particularly critical in the case of ancient languages, where lack of data and long diachronic span make it harder to draw a clear distinction between polysemy and semantic change, and current systems perform poorly on these languages. We develop GASC, a dynamic semantic change model that leverages categorical metadata about the texts' genre information to boost inference and uncover the evolution of meanings in Ancient Greek corpora. In a new evaluation framework, we show that our model achieves improved predictive performance compared to the state of the art.

Bayesian optimal experimental design (BOED) is a principled framework for making efficient use of limited experimental resources. Unfortunately, its applicability is hampered by the difficulty of obtaining accurate estimates of the expected information gain (EIG) of an experiment. To address this, we introduce several classes of fast EIG estimators suited to the experiment design context by building on ideas from variational inference and mutual information estimation. We show theoretically and empirically that these estimators can provide significant gains in speed and accuracy over previous approaches. We demonstrate the practicality of our approach via a number of experiments, including an adaptive experiment with human participants.

In the last five years, the financial industry has been impacted by the emergence of digitalization and machine learning. In this article, we explore two methods that have undergone rapid development in recent years: Gaussian processes and Bayesian optimization. Gaussian processes can be seen as a generalization of Gaussian random vectors and are associated with the development of kernel methods. Bayesian optimization is an approach for performing derivative-free global optimization in a small dimension, and uses Gaussian processes to locate the global maximum of a black-box function. The first part of the article reviews these two tools and shows how they are connected. In particular, we focus on the Gaussian process regression, which is the core of Bayesian machine learning, and the issue of hyperparameter selection. The second part is dedicated to two financial applications. We first consider the modeling of the term structure of interest rates. More precisely, we test the fitting method and compare the GP prediction and the random walk model. The second application is the construction of trend-following strategies, in particular the online estimation of trend and covariance windows.

A core problem in statistics and probabilistic machine learning is to compute probability distributions and expectations. This is the fundamental problem of Bayesian statistics and machine learning, which frames all inference as expectations with respect to the posterior distribution. The key challenge is to approximate these intractable expectations. In this tutorial, we review sequential Monte Carlo (SMC), a random-sampling-based class of methods for approximate inference. First, we explain the basics of SMC, discuss practical issues, and review theoretical results. We then examine two of the main user design choices: the proposal distributions and the so called intermediate target distributions. We review recent results on how variational inference and amortization can be used to learn efficient proposals and target distributions. Next, we discuss the SMC estimate of the normalizing constant, how this can be used for pseudo-marginal inference and inference evaluation. Throughout the tutorial we illustrate the use of SMC on various models commonly used in machine learning, such as stochastic recurrent neural networks, probabilistic graphical models, and probabilistic programs.

Testing for conditional independence is a core aspect of constraint-based causal discovery. Although commonly used tests are perfect in theory, they often fail to reject independence in practice, especially when conditioning on multiple variables. We focus on discrete data and propose a new test based on the notion of algorithmic independence that we instantiate using stochastic complexity. Amongst others, we show that our proposed test, SCI, is an asymptotically unbiased as well as $L_2$ consistent estimator for conditional mutual information (CMI). Further, we show that SCI can be reformulated to find a sensible threshold for CMI that works well on limited samples. Empirical evaluation shows that SCI has a lower type II error than commonly used tests. As a result, we obtain a higher recall when we use SCI in causal discovery algorithms, without compromising the precision.

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.