Bayesian methods are appealing in their flexibility in modeling complex data and ability in capturing uncertainty in parameters. However, when Bayes' rule does not result in tractable closed-form, most approximate inference algorithms lack either scalability or rigorous guarantees. To tackle this challenge, we propose a simple yet provable algorithm, \emph{Particle Mirror Descent} (PMD), to iteratively approximate the posterior density. PMD is inspired by stochastic functional mirror descent where one descends in the density space using a small batch of data points at each iteration, and by particle filtering where one uses samples to approximate a function. We prove result of the first kind that, with $m$ particles, PMD provides a posterior density estimator that converges in terms of $KL$-divergence to the true posterior in rate $O(1/\sqrt{m})$. We demonstrate competitive empirical performances of PMD compared to several approximate inference algorithms in mixture models, logistic regression, sparse Gaussian processes and latent Dirichlet allocation on large scale datasets.

What are the limits of automated Twitter sentiment classification? We analyze a large set of manually labeled tweets in different languages, use them as training data, and construct automated classification models. It turns out that the quality of classification models depends much more on the quality and size of training data than on the type of the model trained. Experimental results indicate that there is no statistically significant difference between the performance of the top classification models. We quantify the quality of training data by applying various annotator agreement measures, and identify the weakest points of different datasets. We show that the model performance approaches the inter-annotator agreement when the size of the training set is sufficiently large. However, it is crucial to regularly monitor the self- and inter-annotator agreements since this improves the training datasets and consequently the model performance. Finally, we show that there is strong evidence that humans perceive the sentiment classes (negative, neutral, and positive) as ordered.

Neuroimaging research has predominantly drawn conclusions based on classical statistics, including null-hypothesis testing, t-tests, and ANOVA. Throughout recent years, statistical learning methods enjoy increasing popularity, including cross-validation, pattern classification, and sparsity-inducing regression. These two methodological families used for neuroimaging data analysis can be viewed as two extremes of a continuum. Yet, they originated from different historical contexts, build on different theories, rest on different assumptions, evaluate different outcome metrics, and permit different conclusions. This paper portrays commonalities and differences between classical statistics and statistical learning with their relation to neuroimaging research. The conceptual implications are illustrated in three common analysis scenarios. It is thus tried to resolve possible confusion between classical hypothesis testing and data-guided model estimation by discussing their ramifications for the neuroimaging access to neurobiology.

Something with BUGS or JAGS or (best of all) STAN code examples would be greatly appreciated.

In an Estimation problem, looking at a data to derive any inference about a'characteristic' of a Population, this approach mainly uses a sample taken at'random' from a collection of these similar items. An'estimate' of that characteristic (also known as a parameter) of the collection (or Universe, Population), is computed from that sample. This estimate is then tested to find out how close it might be to the original parameter, which is usually unknown. Graphical methods such EDA (Exploratory Data Analysis) are also used to study and guess the nature of the characteristic in the population, based on the data from the sample. Sampling is repeated or replicated several times, to reduce the error in the estimate.

The modern data analyst must cope with data encoded in various forms, vectors, matrices, strings, graphs, or more. Consequently, statistical and machine learning models tailored to different data encodings are important. We focus on data encoded as normalized vectors, so that their "direction" is more important than their magnitude. Specifically, we consider high-dimensional vectors that lie either on the surface of the unit hypersphere or on the real projective plane. For such data, we briefly review common mathematical models prevalent in machine learning, while also outlining some technical aspects, software, applications, and open mathematical challenges.

We present algorithms to effectively represent a set of Markov decision processes (MDPs), whose optimal policies have already been learned, by a smaller source subset for lifelong, policy-reuse-based transfer learning in reinforcement learning. This is necessary when the number of previous tasks is large and the cost of measuring similarity counteracts the benefit of transfer. The source subset forms an `$\epsilon$-net' over the original set of MDPs, in the sense that for each previous MDP $M_p$, there is a source $M^s$ whose optimal policy has $<\epsilon$ regret in $M_p$. Our contributions are as follows. We present EXP-3-Transfer, a principled policy-reuse algorithm that optimally reuses a given source policy set when learning for a new MDP. We present a framework to cluster the previous MDPs to extract a source subset. The framework consists of (i) a distance $d_V$ over MDPs to measure policy-based similarity between MDPs; (ii) a cost function $g(\cdot)$ that uses $d_V$ to measure how good a particular clustering is for generating useful source tasks for EXP-3-Transfer and (iii) a provably convergent algorithm, MHAV, for finding the optimal clustering. We validate our algorithms through experiments in a surveillance domain.

Sure, it's a neural net, although someone who felt that it wasn't could probably make that argument. Bottom line - there aren't a lot of fundamentalists who will care a lot about a strong line discriminating what is and is not an instance of machine learning method X. Using a convolutional network as, effectively, a hierarchical set of image filters has certainly been done. You might have some trouble training it with a top level model that had problematic derivatives, and so had weird backprop issues. Realistically, a lot of work has involved training a deep convolutional net on a task, then cutting off the top fully connected layer, and instead taking the inputs as features for another kind of classifier (usually an SVM) to squeeze a little extra performance.

You could learn a discretization, or codebook, of your word2vec features. For example, you could run k-means on all of them (well, all your training word2vec features), then treat each one as a single instance of one of k words. Naive bayes proceeds naturally from documents as histograms of these words, and you don't even have to normalize the word counts. But yeah, it's adding another step, and another parameter (k), and discretization can throw away specificity.

Dynamic Bayesian networks (DBNs) are a general model for stochastic processes with partially observed states. Belief filtering in DBNs is the task of inferring the belief state (i.e. the probability distribution over process states) based on incomplete and noisy observations. This can be a hard problem in complex processes with large state spaces. In this article, we explore the idea of accelerating the filtering task by automatically exploiting causality in the process. We consider a specific type of causal relation, called passivity, which pertains to how state variables cause changes in other variables. We present the Passivity-based Selective Belief Filtering (PSBF) method, which maintains a factored belief representation and exploits passivity to perform selective updates over the belief factors. PSBF produces exact belief states under certain assumptions and approximate belief states otherwise, where the approximation error is bounded by the degree of uncertainty in the process. We show empirically, in synthetic processes with varying sizes and degrees of passivity, that PSBF is faster than several alternative methods while achieving competitive accuracy. Furthermore, we demonstrate how passivity occurs naturally in a complex system such as a multi-robot warehouse, and how PSBF can exploit this to accelerate the filtering task.