Lifted inference reduces the complexity of inference in relational probabilistic models by identifying groups of constants (or atoms) which behave symmetric to each other. A number of techniques have been proposed in the literature for lifting marginal as well MAP inference. We present the first application of lifting rules for marginal-MAP (MMAP), an important inference problem in models having latent (random) variables. Our main contribution is two fold: (1) we define a new equivalence class of (logical) variables, called Single Occurrence for MAX (SOM), and show that solution lies at extreme with respect to the SOM variables, i.e., predicate groundings differing only in the instantiation of the SOM variables take the same truth value (2) we define a sub-class {\em SOM-R} (SOM Reduce) and exploit properties of extreme assignments to show that MMAP inference can be performed by reducing the domain of SOM-R variables to a single constant.We refer to our lifting technique as the {\em SOM-R} rule for lifted MMAP. Combined with existing rules such as decomposer and binomial, this results in a powerful framework for lifted MMAP. Experiments on three benchmark domains show significant gains in both time and memory compared to ground inference as well as lifted approaches not using SOM-R.

A subtle difference between propositional and relational data is that in many relational models, marginal probabilities depend on the population or domain size. This paper connects the dependence on population size to the classic notion of projectivity from statistical theory: Projectivity implies that relational predictions are robust with respect to changes in domain size. We discuss projectivity for a number of common SRL systems, and identify syntactic fragments that are guaranteed to yield projective models. The syntactic conditions are restrictive, which suggests that projectivity is difficult to achieve in SRL, and care must be taken when working with different domain sizes.

In probabilistic reasoning, the traditionally discrete domain has been elevated to the hybrid domain encompassing additionally continuous random variables. Inference in the hybrid domain, however, usually necessitates to condone trade-offs on either the inference on discrete or continuous random variables. We introduce a novel approach based on weighted model integration and algebraic model counting that circumvents these trade-offs. We then show how it supports knowledge compilation and exact probabilistic inference. Moreover, we introduce the hybrid probabilistic logic programming language HAL-ProbLog, an extension of ProbLog, to which we apply our inference approach.

Data scientist Stefano Cosentino observed in a post that the Bayesian approach leans more towards the distributions associated with each parameter. For instance, he writes that the two parameters depicted below, as shown by the Gaussian curves after a trained Bayesian network has converged. Hence the Bayesian approach, where the parameters are unknown quantities can be considered as random variables. University of Buffalo's paper defines the Bayesian approach to uncertainty, which treats all uncertain quantities as random variables and uses the laws of probability to manipulate those uncertain quantities. Hence, the right Bayesian approach integrates over all uncertain quantities rather than optimise them, states the paper.

In the last few months, I have had several people contact me about their enthusiasm for venturing into the world of data science and using Machine Learning (ML) techniques to probe statistical regularities and build impeccable data-driven products. However, I've observed that some actually lack the necessary mathematical intuition and framework to get useful results. This is the main reason I decided to write this blog post. Recently, there has been an upsurge in the availability of many easy-to-use machine and deep learning packages such as scikit-learn, Weka, Tensorflow etc. Machine Learning theory is a field that intersects statistical, probabilistic, computer science and algorithmic aspects arising from learning iteratively from data and finding hidden insights which can be used to build intelligent applications. Despite the immense possibilities of Machine and Deep Learning, a thorough mathematical understanding of many of these techniques is necessary for a good grasp of the inner workings of the algorithms and getting good results.

Bayesian optimization has emerged as a strong candidate tool for global optimization of functions with expensive evaluation costs. However, due to the dynamic nature of research in Bayesian approaches, and the evolution of computing technology, using Bayesian optimization in a parallel computing environment remains a challenge for the non-expert. In this report, I review the state-of-the-art in parallel and scalable Bayesian optimization methods. In addition, I propose practical ways to avoid a few of the pitfalls of Bayesian optimization, such as oversampling of edge parameters and over-exploitation of high performance parameters. Finally, I provide relatively simple, heuristic algorithms, along with their open source software implementations, that can be immediately and easily deployed in any computing environment.

This paper is based on a previous publication [29]. Our work extends exception mining and outlier detection to the case of object-relational data. Object-relational data represent a complex heterogeneous network [12], which comprises objects of different types, links among these objects, also of different types, and attributes of these links. This special structure prohibits a direct vectorial data representation. We follow the well-established Exceptional Model Mining framework, which leverages machine learning models for exception mining: A object is exceptional to the extent that a model learned for the object data differs from a model learned for the general population. Exceptional objects can be viewed as outliers. We apply state of-the-art probabilistic modelling techniques for object-relational data that construct a graphical model (Bayesian network), which compactly represents probabilistic associations in the data. A new metric, derived from the learned object-relational model, quantifies the extent to which the individual association pattern of a potential outlier deviates from that of the whole population. The metric is based on the likelihood ratio of two parameter vectors: One that represents the population associations, and another that represents the individual associations. Our method is validated on synthetic datasets and on real-world data sets about soccer matches and movies. Compared to baseline methods, our novel transformed likelihood ratio achieved the best detection accuracy on all datasets.

New technologies have enabled the investigation of biology and human health at an unprecedented scale and in multiple dimensions. These dimensions include myriad properties describing genome, epigenome, transcriptome, microbiome, phenotype, and lifestyle. No single data type, however, can capture the complexity of all the factors relevant to understanding a phenomenon such as a disease. Integrative methods that combine data from multiple technologies have thus emerged as critical statistical and computational approaches. The key challenge in developing such approaches is the identification of effective models to provide a comprehensive and relevant systems view. An ideal method can answer a biological or medical question, identifying important features and predicting outcomes, by harnessing heterogeneous data across several dimensions of biological variation. In this Review, we describe the principles of data integration and discuss current methods and available implementations. We provide examples of successful data integration in biology and medicine. Finally, we discuss current challenges in biomedical integrative methods and our perspective on the future development of the field.

Methods for reasoning under uncertainty are a key building block of accurate and reliable machine learning systems. Bayesian methods provide a general framework to quantify uncertainty. However, because of model misspecification and the use of approximate inference, Bayesian uncertainty estimates are often inaccurate -- for example, a 90% credible interval may not contain the true outcome 90% of the time. Here, we propose a simple procedure for calibrating any regression algorithm; when applied to Bayesian and probabilistic models, it is guaranteed to produce calibrated uncertainty estimates given enough data. Our procedure is inspired by Platt scaling and extends previous work on classification. We evaluate this approach on Bayesian linear regression, feedforward, and recurrent neural networks, and find that it consistently outputs well-calibrated credible intervals while improving performance on time series forecasting and model-based reinforcement learning tasks.

We present a learning theory for the training of a linear system operator having an input compositional variable and propose a Bayesian inversion method for inferring the unknown variable from an output of a noisy linear system. We assume that we have partial or even no knowledge of the operator but have training data of input and ouput. A compositional variable satisfies the constraints that the elements of the variable are all non-negative and sum to unity. We quantified the uncertainty in the trained operator and present the convergence rates of training in explicit forms for several interesting cases under stochastic compositional models. The trained linear operator with the covariance matrix, estimated from the training set of pairs of ground-truth input and noisy output data, is further used in evaluation of posterior uncertainty of the solution. This posterior uncertainty clearly demonstrates uncertainty propagation from noisy training data and addresses possible mismatch between the true operator and the estimated one in the final solution.