The functions of proteins and RNAs are determined by a myriad of interactions between their constituent residues, but most quantitative models of how molecular phenotype depends on genotype must approximate this by simple additive effects. While recent models have relaxed this constraint to also account for pairwise interactions, these approaches do not provide a tractable path towards modeling higher-order dependencies. Here, we show how latent variable models with nonlinear dependencies can be applied to capture beyond-pairwise constraints in biomolecules. We present a new probabilistic model for sequence families, DeepSequence, that can predict the effects of mutations across a variety of deep mutational scanning experiments significantly better than site independent or pairwise models that are based on the same evolutionary data. The model, learned in an unsupervised manner solely from sequence information, is grounded with biologically motivated priors, reveals latent organization of sequence families, and can be used to extrapolate to new parts of sequence space.

Accurate diagnosis of psychiatric disorders plays a critical role in improving quality of life for patients and potentially supports the development of new treatments. Many studies have been conducted on machine learning techniques that seek brain imaging data for specific biomarkers of disorders. These studies have encountered the following dilemma: An end-to-end classification overfits to a small number of high-dimensional samples but unsupervised feature-extraction has the risk of extracting a signal of no interest. In addition, such studies often provided only diagnoses for patients without presenting the reasons for these diagnoses. This study proposed a deep neural generative model of resting-state functional magnetic resonance imaging (fMRI) data. The proposed model is conditioned by the assumption of the subject's state and estimates the posterior probability of the subject's state given the imaging data, using Bayes' rule. This study applied the proposed model to diagnose schizophrenia and bipolar disorders. Diagnosis accuracy was improved by a large margin over competitive approaches, namely a support vector machine, logistic regression, and multilayer perceptron with or without unsupervised feature-extractors in addition to a Gaussian mixture model. The proposed model visualizes brain regions largely related to the disorders, thus motivating further biological investigation.

Scientific publications have evolved several features for mitigating vocabulary mismatch when indexing, retrieving, and computing similarity between articles. These mitigation strategies range from simply focusing on high-value article sections, such as titles and abstracts, to assigning keywords, often from controlled vocabularies, either manually or through automatic annotation. Various document representation schemes possess different cost-benefit tradeoffs. In this paper, we propose to model different representations of the same article as translations of each other, all generated from a common latent representation in a multilingual topic model. We start with a methodological overview on latent variable models for parallel document representations that could be used across many information science tasks. We then show how solving the inference problem of mapping diverse representations into a shared topic space allows us to evaluate representations based on how topically similar they are to the original article. In addition, our proposed approach provides means to discover where different concept vocabularies require improvement.

Dynamic Boltzmann Machine (DyBM) has been shown highly efficient to predict time-series data. Gaussian DyBM is a DyBM that assumes the predicted data is generated by a Gaussian distribution whose first-order moment (mean) dynamically changes over time but its second-order moment (variance) is fixed. However, in many financial applications, the assumption is quite limiting in two aspects. First, even when the data follows a Gaussian distribution, its variance may change over time. Such variance is also related to important temporal economic indicators such as the market volatility. Second, financial time-series data often requires learning datasets generated by the generalized Gaussian distribution with an additional shape parameter that is important to approximate heavy-tailed distributions. Addressing those aspects, we show how to extend DyBM that results in significant performance improvement in predicting financial time-series data.

We derive a new Bayesian Information Criterion (BIC) from first principles by formulating the problem of estimating the number of clusters in an observed data set as maximization of the posterior probability of the candidate models. Given that some mild assumptions are satisfied, we provide a general BIC expression for a broad class of data distributions. This serves as an important milestone when deriving the BIC for specific data distributions. Along this line, we provide a closed-form BIC expression for multivariate Gaussian distributed observations. We show that incorporating data structure of the clustering problem into the derivation of the BIC results in an expression whose penalty term is different from that of the original BIC. We propose a two-step cluster enumeration algorithm. First, a model-based unsupervised learning algorithm partitions the data according to a given set of candidate models. Subsequently, the optimal cluster number is determined as the one associated to the model for which the proposed BIC is maximal. The performance of the proposed criterion is tested using synthetic and real data sets. Despite the fact that the original BIC is a generic criterion which does not include information about the specific model selection problem at hand, it has been widely used in the literature to estimate the number of clusters in an observed data set. We, therefore, consider it as a benchmark comparison. Simulation results show that our proposed criterion outperforms the existing cluster enumeration methods that are based on the original BIC.

Critical to evaluating the capacity, scalability, and availability of web systems are realistic web traffic generators. Web traffic generation is a classic research problem, no generator accounts for the characteristics of web robots or crawlers that are now the dominant source of traffic to a web server. Administrators are thus unable to test, stress, and evaluate how their systems perform in the face of ever increasing levels of web robot traffic. To resolve this problem, this paper introduces a novel approach to generate synthetic web robot traffic with high fidelity. It generates traffic that accounts for both the temporal and behavioral qualities of robot traffic by statistical and Bayesian models that are fitted to the properties of robot traffic seen in web logs from North America and Europe. We evaluate our traffic generator by comparing the characteristics of generated traffic to those of the original data. We look at session arrival rates, inter-arrival times and session lengths, comparing and contrasting them between generated and real traffic. Finally, we show that our generated traffic affects cache performance similarly to actual traffic, using the common LRU and LFU eviction policies.

The holy trinity when it comes to being Bayesian. I will provide my experience in using the first two packages and my high level opinion of the third (haven't used it in practice). Of course then there is the mad men (old professors who are becoming irrelevant) who actually do their own Gibbs sampling. You specify the generative model for the data. You feed in the data as observations and then it samples from the posterior of the data for you.

What do most effective marketing campaigns have in common? Let us suppose that a company wants to perform a direct marketing campaign to get a response (like a subscription or a purchase) from users. It wants to run a marketing campaign for around 10,000 users out of which only 1,000 users are expected to respond. But the company doesn't have a budget to reach out to all the 10,000 customers. To minimize the cost, the company wants to reach out to the smallest number of customers as possible but at the same time reach out to most (user defined) of the customers who are likely to respond.

Sample-based tree search (SBTS) is an approach to solving Markov decision problems based on constructing a lookahead search tree using random samples from a generative model of the MDP. It encompasses Monte Carlo tree search (MCTS) algorithms like UCT as well as algorithms such as sparse sampling. SBTS is well-suited to solving MDPs with large state spaces due to the relative insensitivity of SBTS algorithms to the size of the state space. The limiting factor in the performance of SBTS tends to be the exponential dependence of sample complexity on the depth of the search tree. The number of samples required to build a search tree is O((|A|B)^d), where |A| is the number of available actions, B is the number of possible random outcomes of taking an action, and d is the depth of the tree. State abstraction can be used to reduce B by aggregating random outcomes together into abstract states. Recent work has shown that abstract tree search often performs substantially better than tree search conducted in the ground state space. This paper presents a theoretical and empirical evaluation of tree search with both fixed and adaptive state abstractions. We derive a bound on regret due to state abstraction in tree search that decomposes abstraction error into three components arising from properties of the abstraction and the search algorithm. We describe versions of popular SBTS algorithms that use fixed state abstractions, and we introduce the Progressive Abstraction Refinement in Sparse Sampling (PARSS) algorithm, which adapts its abstraction during search. We evaluate PARSS as well as sparse sampling with fixed abstractions on 12 experimental problems, and find that PARSS outperforms search with a fixed abstraction and that search with even highly inaccurate fixed abstractions outperforms search without abstraction. These results establish progressive abstraction refinement as a promising basis for new tree search algorithms, and we propose directions for future work within the progressive refinement framework.

This paper introduces the R package sgmcmc; which can be used for Bayesian inference on problems with large datasets using stochastic gradient Markov chain Monte Carlo (SGMCMC). Traditional Markov chain Monte Carlo (MCMC) methods, such as Metropolis-Hastings, are known to run prohibitively slowly as the dataset size increases. SGMCMC solves this issue by only using a subset of data at each iteration. SGMCMC requires calculating gradients of the log likelihood and log priors, which can be time consuming and error prone to perform by hand. The sgmcmc package calculates these gradients itself using automatic differentiation, making the implementation of these methods much easier. To do this, the package uses the software library TensorFlow, which has a variety of statistical distributions and mathematical operations as standard, meaning a wide class of models can be built using this framework. SGMCMC has become widely adopted in the machine learning literature, but less so in the statistics community. We believe this may be partly due to lack of software; this package aims to bridge this gap.