Learning and memory in the brain are implemented by complex, time-varying changes in neural circuitry. The computational rules according to which synaptic weights change over time are the subject of much research, and are not precisely understood. Until recently, limitations in experimental methods have made it challenging to test hypotheses about synaptic plasticity on a large scale. However, as such data become available and these barriers are lifted, it becomes necessary to develop analysis techniques to validate plasticity models. Here, we present a highly extensible framework for modeling arbitrary synaptic plasticity rules on spike train data in populations of interconnected neurons. We treat synaptic weights as a (potentially nonlinear) dynamical system embedded in a fully-Bayesian generalized linear model (GLM). In addition, we provide an algorithm for inferring synaptic weight trajectories alongside the parameters of the GLM and of the learning rules. Using this method, we perform model comparison of two proposed variants of the well-known spike-timing-dependent plasticity (STDP) rule, where nonlinear effects play a substantial role. On synthetic data generated from the biophysical simulator NEURON, we show that we can recover the weight trajectories, the pattern of connectivity, and the underlying learning rules.

Stochastic variational inference (SVI) uses stochastic optimization to scale up Bayesian computation to massive data. We present an alternative perspective on SVI as approximate parallel coordinate ascent. SVI trades-off bias and variance to step close to the unknown true coordinate optimum given by batch variational Bayes (VB). We define a model to automate this process. The model infers the location of the next VB optimum from a sequence of noisy realizations. As a consequence of this construction, we update the variational parameters using Bayes rule, rather than a hand-crafted optimization schedule. When our model is a Kalman filter this procedure can recover the original SVI algorithm and SVI with adaptive steps. We may also encode additional assumptions in the model, such as heavy-tailed noise. By doing so, our algorithm outperforms the original SVI schedule and a state-of-the-art adaptive SVI algorithm in two diverse domains.

Video summarization is a challenging problem with great application potential. Whereas prior approaches, largely unsupervised in nature, focus on sampling useful frames and assembling them as summaries, we consider video summarization as a supervised subset selection problem. Our idea is to teach the system to learn from human-created summaries how to select informative and diverse subsets, so as to best meet evaluation metrics derived from human-perceived quality. To this end, we propose the sequential determinantal point process (seqDPP), a probabilistic model for diverse sequential subset selection. Our novel seqDPP heeds the inherent sequential structures in video data, thus overcoming the deficiency of the standard DPP, which treats video frames as randomly permutable items. Meanwhile, seqDPP retains the power of modeling diverse subsets, essential for summarization. Our extensive results of summarizing videos from 3 datasets demonstrate the superior performance of our method, compared to not only existing unsupervised methods but also naive applications of the standard DPP model.

It has been long argued that, because of inherent ambiguity and noise, the brain needs to represent uncertainty in the form of probability distributions. The neural encodingof such distributions remains however highly controversial. Here we present a novel circuit model for representing multidimensional real-valued distributions usinga spike based spatiotemporal code. Our model combines the computational advantagesof the currently competing models for probabilistic codes and exhibits realistic neural responses along a variety of classic measures. Furthermore, themodel highlights the challenges associated with interpreting neural activity in relation to behavioral uncertainty and points to alternative populationlevel approachesfor the experimental validation of distributed representations. Core brain computations, such as sensory perception, have been successfully characterized as probabilistic inference,whereby sensory stimuli are interpreted in terms of the objects or features that gave rise to them [1, 2].

In many problem settings, parameter vectors are not merely sparse, but dependent in such a way that non-zero coefficients tend to cluster together. We refer to this form of dependency as “region sparsity”. Classical sparse regression methods, such as the lasso and automatic relevance determination (ARD), model parameters as independent a priori, and therefore do not exploit such dependencies. Here we introduce a hierarchical model for smooth, region-sparse weight vectors and tensors in a linear regression setting. Our approach represents a hierarchical extension of the relevance determination framework, where we add a transformed Gaussian process to model the dependencies between the prior variances of regression weights. We combine this with a structured model of the prior variances of Fourier coefficients, which eliminates unnecessary high frequencies. The resulting prior encourages weights to be region-sparse in two different bases simultaneously. We develop efficient approximate inference methods and show substantial improvements over comparable methods (e.g., group lasso and smooth RVM) for both simulated and real datasets from brain imaging.

We propose a technique for decomposing the parameter learning problem in Bayesian networks into independent learning problems. Our technique applies to incomplete datasets and exploits variables that are either hidden or observed in the given dataset. We show empirically that the proposed technique can lead to orders-of-magnitude savings in learning time. We explain, analytically and empirically, the reasons behind our reported savings, and compare the proposed technique to related ones that are sometimes used by inference algorithms.

We address the problem of deciding whether a causal or probabilistic query is estimable from data corrupted by missing entries, given a model of missingness process.We extend the results of Mohan et al. [2013] by presenting more general conditions for recovering probabilistic queries of the form P(y x) and P(y,x) as well as causal queries of the form P(y do(x)). We show that causal queries may be recoverable even when the factors in their identifying estimands are not recoverable. Specifically, we derive graphical conditions for recovering causal effects of the form P(y do(x)) when Y and its missingness mechanism are not d-separable. Finally, we apply our results toproblems of attrition and characterize the recovery of causal effects from data corrupted by attrition.

The Indian Buffet Process is a versatile statistical tool for modeling distributions over binary matrices. We provide an efficient spectral algorithm as an alternative to costly Variational Bayes and sampling-based algorithms. We derive a novel tensorial characterization of the moments of the Indian Buffet Process proper and for two of its applications. We give a computationally efficient iterative inference algorithm, concentration of measure bounds, and reconstruction guarantees. Our algorithm provides superior accuracy and cheaper computation than comparable Variational Bayesian approach on a number of reference problems.

We reduce a broad class of machine learning problems, usually addressed by EM or sampling, to the problem of finding the $k$ extremal rays spanning the conical hull of a data point set. These $k$ ``anchors'' lead to a global solution and a more interpretable model that can even outperform EM and sampling on generalization error. To find the $k$ anchors, we propose a novel divide-and-conquer learning scheme ``DCA'' that distributes the problem to $\mathcal O(k\log k)$ same-type sub-problems on different low-D random hyperplanes, each can be solved by any solver. For the 2D sub-problem, we present a non-iterative solver that only needs to compute an array of cosine values and its max/min entries. DCA also provides a faster subroutine for other methods to check whether a point is covered in a conical hull, which improves algorithm design in multiple dimensions and brings significant speedup to learning. We apply our method to GMM, HMM, LDA, NMF and subspace clustering, then show its competitive performance and scalability over other methods on rich datasets.

Bayesian observer models are very effective in describing human performance in perceptual tasks, so much so that they are trusted to faithfully recover hidden mental representations of priors, likelihoods, or loss functions from the data. However, the intrinsic degeneracy of the Bayesian framework, as multiple combinations of elements can yield empirically indistinguishable results, prompts the question of model identifiability. We propose a novel framework for a systematic testing of the identifiability of a significant class of Bayesian observer models, with practical applications for improving experimental design. We examine the theoretical identifiability of the inferred internal representations in two case studies. First, we show which experimental designs work better to remove the underlying degeneracy in a time interval estimation task. Second, we find that the reconstructed representations in a speed perception task under a slow-speed prior are fairly robust.