Mechanistic models of single-neuron dynamics have been extensively studied in computational neuroscience. However, identifying which models can quantitatively reproduce empirically measured data has been challenging. We propose to overcome this limitation by using likelihood-free inference approaches (also known as Approximate Bayesian Computation, ABC) to perform full Bayesian inference on single-neuron models. Our approach builds on recent advances in ABC by learning a neural network which maps features of the observed data to the posterior distribution over parameters. We learn a Bayesian mixture-density network approximating the posterior over multiple rounds of adaptively chosen simulations. Furthermore, we propose an efficient approach for handling missing features and parameter settings for which the simulator fails, as well as a strategy for automatically learning relevant features using recurrent neural networks. On synthetic data, our approach efficiently estimates posterior distributions and recovers ground-truth parameters. On in-vitro recordings of membrane voltages, we recover multivariate posteriors over biophysical parameters, which yield model-predicted voltage traces that accurately match empirical data. Our approach will enable neuroscientists to perform Bayesian inference on complex neuron models without having to design model-specific algorithms, closing the gap between mechanistic and statistical approaches to single-neuron modelling.

Generalized linear models (GLMs)---such as logistic regression, Poisson regression, and robust regression---provide interpretable models for diverse data types. Probabilistic approaches, particularly Bayesian ones, allow coherent estimates of uncertainty, incorporation of prior information, and sharing of power across experiments via hierarchical models. In practice, however, the approximate Bayesian methods necessary for inference have either failed to scale to large data sets or failed to provide theoretical guarantees on the quality of inference. We propose a new approach based on constructing polynomial approximate sufficient statistics for GLMs (PASS-GLM). We demonstrate that our method admits a simple algorithm as well as trivial streaming and distributed extensions that do not compound error across computations. We provide theoretical guarantees on the quality of point (MAP) estimates, the approximate posterior, and posterior mean and uncertainty estimates. We validate our approach empirically in the case of logistic regression using a quadratic approximation and show competitive performance with stochastic gradient descent, MCMC, and the Laplace approximation in terms of speed and multiple measures of accuracy---including on an advertising data set with 40 million data points and 20,000 covariates.

We present a novel training framework for neural sequence models, particularly for grounded dialog generation. The standard training paradigm for these models is maximum likelihood estimation (MLE), or minimizing the cross-entropy of the human responses. Across a variety of domains, a recurring problem with MLE trained generative neural dialog models (G) is that they tend to produce'safe' and generic responses like I don't know, I can't tell). In contrast, discriminative dialog models (D) that are trained to rank a list of candidate human responses outperform their generative counterparts; in terms of automatic metrics, diversity, and informativeness of the responses. However, D is not useful in practice since it can not be deployed to have real conversations with users. Our work aims to achieve the best of both worlds -- the practical usefulness of G and the strong performance of D -- via knowledge transfer from D to G. Our primary contribution is an end-to-end trainable generative visual dialog model, where G receives gradients from D as a perceptual (not adversarial) loss of the sequence sampled from G. We leverage the recently proposed Gumbel-Softmax (GS) approximation to the discrete distribution -- specifically, a RNN is augmented with a sequence of GS samplers, which coupled with the straight-through gradient estimator enables end-to-end differentiability. We also introduce a stronger encoder for visual dialog, and employ a self-attention mechanism for answer encoding along with a metric learning loss to aid D in better capturing semantic similarities in answer responses. Overall, our proposed model outperforms state-of-the-art on the VisDial dataset by a significant margin (2.67% on recall@10).

We propose a vector-valued regression problem whose solution is equivalent to the reproducing kernel Hilbert space (RKHS) embedding of the Bayesian posterior distribution. This equivalence provides a new understanding of kernel Bayesian inference. Moreover, the optimization problem induces a new regularization for the posterior embedding estimator, which is faster and has comparable performance to the squared regularization in kernel Bayes' rule. This regularization coincides with a former thresholding approach used in kernel POMDPs whose consistency remains to be established. Our theoretical work solves this open problem and provides consistency analysis in regression settings. Based on our optimizational formulation, we propose a flexible Bayesian posterior regularization framework which for the first time enables us to put regularization at the distribution level. We apply this method to nonparametric state-space filtering tasks with extremely nonlinear dynamics and show performance gains over all other baselines.

In this work, we propose an infinite restricted Boltzmann machine (RBM), whose maximum likelihood estimation (MLE) corresponds to a constrained convex optimization. We consider the Frank-Wolfe algorithm to solve the program, which provides a sparse solution that can be interpreted as inserting a hidden unit at each iteration, so that the optimization process takes the form of a sequence of finite models of increasing complexity. As a side benefit, this can be used to easily and efficiently identify an appropriate number of hidden units during the optimization. The resulting model can also be used as an initialization for typical state-of-the-art RBM training algorithms such as contrastive divergence, leading to models with consistently higher test likelihood than random initialization.

In neuroscience, the similarity matrix of neural activity patterns in response to different sensory stimuli or under different cognitive states reflects the structure of neural representational space. Existing methods derive point estimations of neural activity patterns from noisy neural imaging data, and the similarity is calculated from these point estimations. We show that this approach translates structured noise from estimated patterns into spurious bias structure in the resulting similarity matrix, which is especially severe when signal-to-noise ratio is low and experimental conditions cannot be fully randomized in a cognitive task. We propose an alternative Bayesian framework for computing representational similarity in which we treat the covariance structure of neural activity patterns as a hyper-parameter in a generative model of the neural data, and directly estimate this covariance structure from imaging data while marginalizing over the unknown activity patterns. Converting the estimated covariance structure into a correlation matrix offers a much less biased estimate of neural representational similarity. Our method can also simultaneously estimate a signal-to-noise map that informs where the learned representational structure is supported more strongly, and the learned covariance matrix can be used as a structured prior to constrain Bayesian estimation of neural activity patterns.

We present a unified approach for learning the parameters of Sum-Product networks (SPNs). We prove that any complete and decomposable SPN is equivalent to a mixture of trees where each tree corresponds to a product of univariate distributions. Based on the mixture model perspective, we characterize the objective function when learning SPNs based on the maximum likelihood estimation (MLE) principle and show that the optimization problem can be formulated as a signomial program. We construct two parameter learning algorithms for SPNs by using sequential monomial approximations (SMA) and the concave-convex procedure (CCCP), respectively. The two proposed methods naturally admit multiplicative updates, hence effectively avoiding the projection operation. With the help of the unified framework, we also show that, in the case of SPNs, CCCP leads to the same algorithm as Expectation Maximization (EM) despite the fact that they are different in general.

A key problem in structured output prediction is enabling direct optimization of the task reward function that matters for test evaluation. This paper presents a simple and computationally efficient method that incorporates task reward into maximum likelihood training. We establish a connection between maximum likelihood and regularized expected reward, showing that they are approximately equivalent in the vicinity of the optimal solution. Then we show how maximum likelihood can be generalized by optimizing the conditional probability of auxiliary outputs that are sampled proportional to their exponentiated scaled rewards. We apply this framework to optimize edit distance in the output space, by sampling from edited targets. Experiments on speech recognition and machine translation for neural sequence to sequence models show notable improvements over maximum likelihood baseline by simply sampling from target output augmentations.

In recent years, a rapidly increasing number of applications in practice requires solving non-convex objectives, like training neural networks, learning graphical models, maximum likelihood estimation etc. Though simple heuristics such as gradient descent with very few modifications tend to work well, theoretical understanding is very weak. We consider possibly the most natural class of non-convex functions where one could hope to obtain provable guarantees: functions that are ``approximately convex'', i.e. functions $\tf: \Real^d \to \Real$ for which there exists a \emph{convex function} $f$ such that for all $x$, $|\tf(x) - f(x)| \le \errnoise$ for a fixed value $\errnoise$.

Accurately differentiating between what are truly unpredictably random and systematic changes that occur at random can have profound effect on affect and cognition. To examine the underlying computational principles that guide different learning behavior in an uncertain environment, we compared an R-W model and a Bayesian approach in a visual search task with different volatility levels. Both R-W model and the Bayesian approach reflected an individual's estimation of the environmental volatility, and there is a strong correlation between the learning rate in R-W model and the belief of stationarity in the Bayesian approach in different volatility conditions. In a low volatility condition, R-W model indicates that learning rate positively correlates with lose-shift rate, but not choice optimality (inverted U shape). The Bayesian approach indicates that the belief of environmental stationarity positively correlates with choice optimality, but not lose-shift rate (inverted U shape). In addition, we showed that comparing to Expert learners, individuals with high lose-shift rate (sub-optimal learners) had significantly higher learning rate estimated from R-W model and lower belief of stationarity from the Bayesian model.