Modifying the reward-biased maximum likelihood method originally proposed in the adaptive control literature, we propose novel learning algorithms to handle the explore-exploit trade-off in linear bandits problems as well as generalized linear bandits problems. We develop novel index policies that we prove achieve order-optimality, and show that they achieve empirical performance competitive with the state-of-the-art benchmark methods in extensive experiments. The new policies achieve this with low computation time per pull for linear bandits, and thereby resulting in both favorable regret as well as computational efficiency.

The SIGTYP 2020 shared task (Bjerva et al., 2020) We reach the accuracy of 70.7% on the test data and rank first in the shared task. The task specification envisions a constrained The World Atlas of Language Structures (WALS) and an unconstrained track, where the constrained (Dryer and Haspelmath, 2013) is a database of systems can use only the provided WALS data, over 2,000 languages, which lists structural properties while an unconstrained system can use additional ('features') of each language, gathered from external resources, such as texts or pre-trained word reference grammars.

With a growth in advertisements and cold-messaging we are now receiving a nonstop coherent threads of commercial messages and emails. A user, like you and I, sometimes find it difficult to find a text/email which is actually useful to us or the one which we seek. Detection systems such as Spam detection system are becoming increasingly useful to classify the important data amongst the bundle of raw and undesired data. In this post we'll look at one such detection model, a spam detection model using NLP (natural language processing) and also learn about classification using Naïve Bayes. You can see that we are interested in calculating the posterior probability of P(h d) from the prior probability p(h) with P(D) and P(d h). UCI have an available data set of more than 5000 mixed text messages, click here.

This paper deals with chain graphs (CGs) under the Andersson–Madigan–Perlman (AMP) interpretation. We address the problem of finding a minimal separator in an AMP CG, namely, finding a set Z of nodes that separates a given non-adjacent pair of nodes such that no proper subset of Z separates that pair. We analyze several versions of this problem and offer polynomial time algorithms for each. These include finding a minimal separator from a restricted set of nodes, finding a minimal separator for two given disjoint sets, and testing whether a given separator is minimal. To address the problem of learning the structure of AMP CGs from data, we show that the PC-like algorithm is order dependent, in the sense that the output can depend on the order in which the variables are given. We propose several modifications of the PC-like algorithm that remove part or all of this order-dependence. We also extend the decomposition-based approach for learning Bayesian networks (BNs) to learn AMP CGs, which include BNs as a special case, under the faithfulness assumption. We prove the correctness of our extension using the minimal separator results. Using standard benchmarks and synthetically generated models and data in our experiments demonstrate the competitive performance of our decomposition-based method, called LCD-AMP, in comparison with the (modified versions of) PC-like algorithm. The LCD-AMP algorithm usually outperforms the PC-like algorithm, and our modifications of the PC-like algorithm learn structures that are more similar to the underlying ground truth graphs than the original PC-like algorithm, especially in high-dimensional settings. In particular, we empirically show that the results of both algorithms are more accurate and stabler when the sample size is reasonably large and the underlying graph is sparse

Investigating real-world systems and phenomena typically requires complex models that involve a large number of parameters. Even with sizeable amount of observation data, the high complexity of the model may render accurate parameter estimation impossible. While finding a reliable point estimate of the parameter vector may not be possible in such a case, it may be possible to identify the parameter ranges based on the available data and/or prior system knowledge, or in a more general setting, we may assume a joint distribution of the model parameters. Since different parameter values are possible, this gives rise to an uncertainty class of all possible models [1, 2]. Furthermore, this naturally places the model in a Bayesian framework, where the likelihood of every possible model in the uncertainty class is described by a prior that could be constructed from prior system knowledge and existing data [3, 4]. Given an uncertain model and its uncertainty class, how can one mathematically quantify the amount of uncertainty present in the model? Common approaches include estimating the variance or entropy of the uncertain parameters, as they both provide a simple and intuitive measure of the model uncertainty. However, they both have a critical downside from a practical perspective. In practical applications that involve mathematical modeling of a complex system, one cares about the model as it can serve as a vehicle for designing an effective operator (i.e., controller, classifier, filter) that can act on the system of interest or the data produced therefrom.

We present the Sum-Product Probabilistic Language (SPPL), a new system that automatically delivers exact solutions to a broad range of probabilistic inference queries. SPPL symbolically represents the full distribution on execution traces specified by a probabilistic program using a generalization of sum-product networks. SPPL handles continuous and discrete distributions, many-to-one numerical transformations, and a query language that includes general predicates on random variables. We formalize SPPL in terms of a novel translation strategy from probabilistic programs to a semantic domain of sum-product representations, present new algorithms for exactly conditioning on and computing probabilities of queries, and prove their soundness under the semantics. We present techniques for improving the scalability of translation and inference by automatically exploiting conditional independences and repeated structure in SPPL programs. We implement a prototype of SPPL with a modular architecture and evaluate it on a suite of common benchmarks, which establish that our system is up to 3500x faster than state-of-the-art systems for fairness verification; up to 1000x faster than state-of-the-art symbolic algebra techniques; and can compute exact probabilities of rare events in milliseconds.

We propose a novel data-driven approach to solving a classical statistical mechanics problem: given data on collective motion of particles, characterise the set of free energies associated with the system of particles. We demonstrate empirically that the particle data contains all the information necessary to infer a free energy. While traditional physical modelling seeks to construct analytically tractable approximations, the proposed approach leverages modern Bayesian computational capabilities to accomplish this in a purely data-driven fashion. The Bayesian paradigm permits us to combine underpinning physical principles with simulation data to obtain uncertainty-quantified predictions of the free energy, in the form of a probability distribution over the family of free energies consistent with the observed particle data. In the present work we focus on classical statistical mechanical systems with excluded volume interactions. Using standard coarse-graining methods, our results can be made applicable to systems with realistic attractive-repulsive interactions. We validate our method on a paradigmatic and computationally cheap case of a one-dimensional fluid. With the appropriate particle data, it is possible to learn canonical and grand-canonical representations of the underlying physical system. Extensions to higher-dimensional systems are conceptually straightforward.

Noname manuscript No. (will be inserted by the editor) Abstract Bayesian Additive Regression Trees (BART) 1 Introduction is a tree-based machine learning method that has been successfully applied to regression and classification problems. Bayesian Additive Regression Trees (BART) is a statistical BART assumes regularisation priors on a set of method proposed by Chipman et al (2010) that has trees that work as weak learners and is very flexible for become popular in recent years due to its competitive predicting in the presence of non-linearity and highorder performance on regression and classification problems, interactions. In this paper, we introduce an extension when compared to other supervised machine learning of BART, called Model Trees BART (MOTR-methods, such as Random Forests (RF) (Breiman, 2001) BART), that considers piecewise linear functions at node and Gradient Boosting (GB) (Friedman, 2001). In MOTR-BART, differs from other tree-based methods as it controls the rather than having a unique value at node level for the structure of each tree via a prior distribution and generates prediction, a linear predictor is estimated considering the predictions via an MCMC backfitting algorithm the covariates that have been used as the split variables that is responsible for accepting and rejecting the in the corresponding tree. In our approach, local linearities proposed trees along the iterations.

Bayesian bandits using Thompson Sampling have seen increasing success in recent years. Yet existing value models (of rewards) are misspecified on many real-world problem. We demonstrate this on the User Experience Optimization (UXO) problem, providing a novel formulation as a restless, sleeping bandit with unobserved confounders plus optional stopping. Our case studies show how common misspecifications can lead to sub-optimal rewards, and we provide model extensions to address these, along with a scientific model building process practitioners can adopt or adapt to solve their own unique problems. To our knowledge, this is the first study showing the effects of overdispersion on bandit explore/exploit efficacy, tying the common notions of under- and over-confidence to over- and under-exploration, respectively. We also present the first model to exploit cointegration in a restless bandit, demonstrating that finite regret and fast and consistent optional stopping are possible by moving beyond simpler windowing, discounting, and drift models.

Distance weighted discrimination (DWD) is a linear discrimination method that is particularly well-suited for classification tasks with high-dimensional data. The DWD coefficients minimize an intuitive objective function, which can solved very efficiently using state-of-the-art optimization techniques. However, DWD has not yet been cast into a model-based framework for statistical inference. In this article we show that DWD identifies the mode of a proper Bayesian posterior distribution, that results from a particular link function for the class probabilities and a shrinkage-inducing proper prior distribution on the coefficients. We describe a relatively efficient Markov chain Monte Carlo (MCMC) algorithm to simulate from the true posterior under this Bayesian framework. We show that the posterior is asymptotically normal and derive the mean and covariance matrix of its limiting distribution. Through several simulation studies and an application to breast cancer genomics we demonstrate how the Bayesian approach to DWD can be used to (1) compute well-calibrated posterior class probabilities, (2) assess uncertainty in the DWD coefficients and resulting sample scores, (3) improve power via semi-supervised analysis when not all class labels are available, and (4) automatically determine a penalty tuning parameter within the model-based framework. R code to perform Bayesian DWD is available at https://github.com/lockEF/BayesianDWD .