We propose a topological learning algorithm for the estimation of the conditional dependency structure of large sets of random variables from sparse and noisy data. The algorithm, named Maximally Filtered Clique Forest (MFCF), produces a clique forest and an associated Markov Random Field (MRF) by generalising Prim's minimum spanning tree algorithm. To the best of our knowledge, the MFCF presents three elements of novelty with respect to existing structure learning approaches. The first is the repeated application of a local topological move, the clique expansion, that preserves the decomposability of the underlying graph. Through this move the decomposability and calculation of scores is performed incrementally at the variable (rather than edge) level, and this provides better computational performance and an intuitive application of multivariate statistical tests. The second is the capability to accommodate a variety of score functions and, while this paper is focused on multivariate normal distributions, it can be directly generalised to different types of statistics. Finally, the third is the variable range of allowed clique sizes which is an adjustable topological constraint that acts as a topological penalizer providing a way to tackle sparsity at $l_0$ semi-norm level; this allows a clean decoupling of structure learning and parameter estimation. The MFCF produces a representation of the clique forest, together with a perfect ordering of the cliques and a perfect elimination ordering for the vertices. As an example we propose an application to covariance selection models and we show that the MCFC outperforms the Graphical Lasso for a number of classes of matrices.

There is an abundance of complex dynamic systems that are critical to our daily lives and our society but that are hardly understood, and even with today's possibilities to sense and collect large amounts of experimental data, they are so complex and continuously evolving that it is unlikely that their dynamics will ever be understood in full detail. Nevertheless, through computational tools we can try to make the best possible use of the current technologies and available data. We believe that the most useful models will have to take into account the imbalance between system complexity and available data in the context of limited knowledge or multiple hypotheses. The complex system of biological cells is a prime example of such a system that is studied in systems biology and has motivated the methods presented in this paper. They were developed as part of the DARPA Rapid Threat Assessment (RTA) program, which is concerned with understanding of the mechanism of action (MoA) of toxins or drugs affecting human cells. Using a combination of Gaussian processes and abstract network modeling, we present three fundamentally different machine-learning-based approaches to learn causal relations and synthesize causal networks from high-dimensional time series data. While other types of data are available and have been analyzed and integrated in our RTA work, we focus on transcriptomics (that is gene expression) data obtained from high-throughput microarray experiments in this paper to illustrate capabilities and limitations of our algorithms. Our algorithms make different but overall relatively few biological assumptions, so that they are applicable to other types of biological data and potentially even to other complex systems that exhibit high dimensionality but are not of biological nature.

The Unbiased Learning-to-Rank framework has been recently proposed as a general approach to systematically remove biases, such as position bias, from learning-to-rank models. The method takes two steps - estimating click propensities and using them to train unbiased models. Most common methods proposed in the literature for estimating propensities involve some degree of intervention in the live search engine. An alternative approach proposed recently uses an Expectation Maximization (EM) algorithm to estimate propensities by using ranking features for estimating relevances. In this work we propose a novel method to directly estimate propensities which does not use any intervention in live search or rely on modeling relevance. Rather, we take advantage of the fact that the same query-document pair may naturally change ranks over time. This typically occurs for eCommerce search because of change of popularity of items over time, existence of time dependent ranking features, or addition or removal of items to the index (an item getting sold or a new item being listed). However, our method is general and can be applied to any search engine for which the rank of the same document may naturally change over time for the same query. We derive a simple likelihood function that depends on propensities only, and by maximizing the likelihood we are able to get estimates of the propensities. We apply this method to eBay search data to estimate click propensities for web and mobile search and compare these with estimates using the EM method. We also use simulated data to show that the method gives reliable estimates of the "true" simulated propensities. Finally, we train an unbiased learning-to-rank model for eBay search using the estimated propensities and show that it outperforms both baselines - one without position bias correction and one with position bias correction using the EM method.

If there was something that always frustrated me was not fully understanding Bayesian inference. Sometime last year, I came across an article about a TensorFlow-supported R package for Bayesian analysis, called greta. Back then, I searched for greta tutorials and stumbled on this blog post that praised a textbook called Statistical Rethinking: A Bayesian Course with Examples in R and Stan by Richard McElreath. I had found a solution to my lingering frustration so I bought a copy straight away. I spent the last few months reading it cover to cover and solving the proposed exercises, which are heavily based on the rethinking package. I cannot recommend it highly enough to whoever seeks a solid grip on Bayesian statistics, both in theory and application. This post ought to be my most gratifying blogging experience so far, in that I am essentially reporting my own recent learning. I am convinced this will make the storytelling all the more effective. As a demonstration, the female cuckoo reproductive output data recently analysed by Riehl et al., 2019 [1] will be modelled using In the process, we will conduct the MCMC sampling, visualise posterior distributions, generate predictions and ultimately assess the influence of social parasitism in female reproductive output. You should have some familiarity with standard statistical models. If you need to refresh some basics of probabilities using R have a look into my first post. I hope you enjoy as much as I did!

This survey samples from the ever-growing family of adaptive resonance theory (ART) neural network models used to perform the three primary machine learning modalities, namely, unsupervised, supervised and reinforcement learning. It comprises a representative list from classic to modern ART models, thereby painting a general picture of the architectures developed by researchers over the past 30 years. The learning dynamics of these ART models are briefly described, and their distinctive characteristics such as code representation, long-term memory and corresponding geometric interpretation are discussed. Useful engineering properties of ART (speed, configurability, explainability, parallelization and hardware implementation) are examined along with current challenges. Finally, a compilation of online software libraries is provided. It is expected that this overview will be helpful to new and seasoned ART researchers.

We consider Bayesian inference when only a limited number of noisy log-likelihood evaluations can be obtained. This occurs for example when complex simulator-based statistical models are fitted to data, and synthetic likelihood (SL) is used to form the noisy log-likelihood estimates using computationally costly forward simulations. We frame the inference task as a Bayesian sequential design problem, where the log-likelihood function is modelled with a hierarchical Gaussian process (GP) surrogate model, which is used to efficiently select additional log-likelihood evaluation locations. Motivated by recent progress in batch Bayesian optimisation, we develop various batch-sequential strategies where multiple simulations are adaptively selected to minimise either the expected or median loss function measuring the uncertainty in the resulting posterior. We analyse the properties of the resulting method theoretically and empirically. Experiments with toy problems and three simulation models suggest that our method is robust, highly parallelisable, and sample-efficient.

Many real world tasks exhibit rich structure that is repeated across different parts of the state space or in time. In this work we study the possibility of leveraging such repeated structure to speed up and regularize learning. We start from the KL regularized expected reward objective which introduces an additional component, a default policy. Instead of relying on a fixed default policy, we learn it from data. But crucially, we restrict the amount of information the default policy receives, forcing it to learn reusable behaviours that help the policy learn faster. We formalize this strategy and discuss connections to information bottleneck approaches and to the variational EM algorithm. We present empirical results in both discrete and continuous action domains and demonstrate that, for certain tasks, learning a default policy alongside the policy can significantly speed up and improve learning.

In this paper, we propose an intelligence approach based on fuzzy logic to modeling human intelligence in washing clothes. At first, an intelligent feedback loop is designed for perception-based sensing of dirt inspired by human color understanding. Then, when color stains leak out of some colored clothes the human probabilistic decision making is computationally modeled to detect this stain leakage and thus the problem of recognizing dirt from stain can be considered in the washing process. Finally, we discuss the fuzzy control of washing clothes and design and simulate a smart controller based on the fuzzy intelligence feedback loop.

Odor identification is an important area in a wide range of industries like cosmetics, food, beverages and medical diagnosis among others. Odor detection could be done through an array of gas sensors conformed as an electronic nose where a data acquisition module converts sensor signals to a standard output to be analyzed. To facilitate odors detection a system is required for the identification. This paper presents the results of an automated odor identification process implemented by a fuzzy system and an electronic nose. First, an electronic nose prototype is manufactured to detect organic compounds vapor using an array of five tin dioxide gas sensors, an arduino uno board is used as a data acquisition section. Second, an intelligent module with a fuzzy system is considered for the identification of the signals received by the electronic nose. This solution proposes a system to identify odors by using a personal computer. Results show an acceptable precision.

The problem at the heart of this tutorial consists in modeling the path choice behavior of network users. This problem has extensively been studied in transportation science and econometrics, where it is known as the route choice problem. In this literature, individuals' choice of paths are typically predicted from discrete choice models. The aim of this tutorial is to present this problem from the novel and more general perspective of inverse optimization, in order to describe the modeling approaches proposed in related research areas and thereby motivate the use of so-called recursive models. The latter have the advantage of predicting path choices without generating choice sets. In this paper, we contextualize discrete choice models as a probabilistic approach to an inverse shortest path problem with noisy data, highlighting that recursive discrete choice models in particular originate from viewing the inner shortest path problem as a parametric Markov Decision Process. We also illustrate through simple numerical examples that recursive models overcome issues associated with the path-based discrete choice models commonly found in the transportation literature.