An open question in systems and computational neuroscience is how neural circuits accumulate evidence towards a decision. Fitting models of decision-making theory to neural activity helps answer this question, but current approaches limit the number of these models that we can fit to neural data. Here we propose a unifying framework for modeling neural activity during decision-making tasks. The framework includes the canonical drift-diffusion model and enables extensions such as multi-dimensional accumulators, variable and collapsing boundaries, and discrete jumps. Our framework is based on constraining the parameters of recurrent state-space models, for which we introduce a scalable variational Laplace-EM inference algorithm. We applied the modeling approach to spiking responses recorded from monkey parietal cortex during two decision-making tasks. We found that a two-dimensional accumulator better captured the trial-averaged responses of a set of parietal neurons than a single accumulator model. Next, we identified a variable lower boundary in the responses of an LIP neuron during a random dot motion task.

The scalable inference for Bayesian nonparametric models with big data is still challenging. Current variational inference methods fail to characterise the correlation structure among latent variables due to the mean-field setting and cannot infer the true posterior dimension because of the universal truncation. To overcome these limitations, we build a general framework to infer Bayesian nonparametric models by maximising the proposed nonparametric evidence lower bound, and then develop a novel approach by combining Monte Carlo sampling and stochastic variational inference framework. Our method has several advantages over the traditional online variational inference method. First, it achieves a smaller divergence between variational distributions and the true posterior by factorising variational distributions under the conditional setting instead of the mean-field setting to capture the correlation pattern. Second, it reduces the risk of underfitting or overfitting by truncating the dimension adaptively rather than using a prespecified truncated dimension for all latent variables. Third, it reduces the computational complexity by approximating the posterior functionally instead of updating the stick-breaking parameters individually. We apply the proposed method on hierarchical Dirichlet process and gamma--Dirichlet process models, two essential Bayesian nonparametric models in topic analysis. The empirical study on three large datasets including arXiv, New York Times and Wikipedia reveals that our proposed method substantially outperforms its competitor in terms of lower perplexity and much clearer topic-words clustering.

When people learn mathematical patterns or sequences, they are able to identify the concepts (or rules) underlying those patterns. Having learned the underlying concepts, humans are also able to generalize those concepts to other numbers, so far as to even identify previously unseen combinations of those rules. Current state-of-the art RNN architectures like LSTMs perform well in predicting successive elements of sequential data, but require vast amounts of training examples. Even with extensive data, these models struggle to generalize concepts. From our behavioral study, we also found that humans are able to disregard noise and identify the underlying rules generating the corrupted sequences. We therefore propose a Bayesian model that captures these human-like learning capabilities to predict next number in a given sequence, better than traditional LSTMs.

Fusion is a common tool for the analysis and utilization of available datasets and so an essential part of data mining and machine learning processes. However, a clear definition of the type of fusion is not always provided due to inconsistent literature. In the following, the process of fusion is defined depending on the fusion components and the abstraction level on which the fusion occurs. The focus in the first part of the paper at hand is on the clear definition of the terminology and the development of an appropriate ontology of the fusion components and the fusion level. In the second part, common fusion techniques are presented.

To solve hard problems, AI relies on a variety of disciplines such as logic, probabilistic reasoning, machine learning and mathematical programming. Although it is widely accepted that solving real-world problems requires an integration amongst these, contemporary representation methodologies offer little support for this. In an attempt to alleviate this situation, we introduce a new declarative programming framework that provides abstractions of well-known problems such as SAT, Bayesian inference, generative models, and convex optimization. The semantics of programs is defined in terms of first-order structures with semiring labels, which allows us to freely combine and integrate problems from different AI disciplines.

There is an increasing desire for autonomous systems to have high levels of robustness and safety, attained through continuously planning and self-repairing online. Underlying this is the need to accurately estimate the system state and diagnose subtle failures. Estimation methods based on hybrid discrete and continuous state models have emerged as a method of precisely computing these estimates. However, existing methods have difficulty scaling to systems with more than a handful of components. Discrete, consistency based state estimation capabilities can scale to this level by combining best-first enumeration and conflict-directed search. While best-first methods have been developed for hybrid estimation, conflict-directed methods have thus far been elusive as conflicts learn inconsistencies from constraint violation, but probabilistic hybrid estimation is relatively unconstrained. In this paper we present an approach to hybrid estimation that unifies best-first enumeration and conflict-directed search through the concept of "bounding" conflicts, an extension of conflicts that represent tighter bounds on the cost of regions of the search space. This paper presents a general best-first enumeration algorithm based on bounding conflicts (A*BC) and a hybrid estimation method using this enumeration algorithm. Experiments show that an A*BC powered state estimator produces estimates up to an order of magnitude faster than the current state of the art, particularly on large systems.

Heterogeneity between training and testing data degrades reproducibility of a well-trained predictive algorithm. In modern applications, how to deploy a trained algorithm in a different domain is becoming an urgent question raised by many domain scientists. In this paper, we propose a reproducible bootstrap aggregating (Rbagging) method coupled with a new algorithm, the iterative nearest neighbor sampler (INNs), effectively drawing bootstrap samples from training data to mimic the distribution of the test data. Rbagging is a general ensemble framework that can be applied to most classifiers. We further propose Rbagging+ to effectively detect anomalous samples in the testing data. Our theoretical results show that the resamples based on Rbagging have the same distribution as the testing data. Moreover, under suitable assumptions, we further provide a general bound to control the test excess risk of the ensemble classifiers. The proposed method is compared with several other popular domain adaptation methods via extensive simulation studies and real applications including medical diagnosis and imaging classifications.

The fate of scientific hypotheses often relies on the ability of a computational model to explain the data, quantified in modern statistical approaches by the likelihood function. The log-likelihood is the key element for parameter estimation and model evaluation. However, the log-likelihood of complex models in fields such as computational biology and neuroscience is often intractable to compute analytically or numerically. In those cases, researchers can often only estimate the log-likelihood by comparing observed data with synthetic observations generated by model simulations. Standard techniques to approximate the likelihood via simulation either use summary statistics of the data or are at risk of producing severe biases in the estimate. Here, we explore another method, inverse binomial sampling (IBS), which can estimate the log-likelihood of an entire data set efficiently and without bias. For each observation, IBS draws samples from the simulator model until one matches the observation. The log-likelihood estimate is then a function of the number of samples drawn. The variance of this estimator is uniformly bounded, achieves the minimum variance for an unbiased estimator, and we can compute calibrated estimates of the variance. We provide theoretical arguments in favor of IBS and an empirical assessment of the method for maximum-likelihood estimation with simulation-based models. As case studies, we take three model-fitting problems of increasing complexity from computational and cognitive neuroscience. In all problems, IBS generally produces lower error in the estimated parameters and maximum log-likelihood values than alternative sampling methods with the same average number of samples. Our results demonstrate the potential of IBS as a practical, robust, and easy to implement method for log-likelihood evaluation when exact techniques are not available.

We propose a formalization of the three-tier causal hierarchy of association, intervention, and counterfactuals as a series of probabilistic logical languages. Our languages are of strictly increasing expressivity, the first capable of expressing quantitative probabilistic reasoning---including conditional independence and Bayesian inference---the second encoding do-calculus reasoning for causal effects, and the third capturing a fully expressive do-calculus for arbitrary counterfactual queries. We give a corresponding series of finitary axiomatizations complete over both structural causal models and probabilistic programs, and show that satisfiability and validity for each language are decidable in polynomial space.

Thompson Sampling is a well established approach to bandit and reinforcement learning problems. However its use in continuum armed bandit problems has received relatively little attention. We provide the first bounds on the regret of Thompson Sampling for continuum armed bandits under weak conditions on the function class containing the true function and sub-exponential observation noise. Our bounds are realised by analysis of the eluder dimension, a recently proposed measure of the complexity of a function class, which has been demonstrated to be useful in bounding the Bayesian regret of Thompson Sampling for simpler bandit problems under sub-Gaussian observation noise. We derive a new bound on the eluder dimension for classes of functions with Lipschitz derivatives, and generalise previous analyses in multiple regards.