When used as a surrogate objective for maximum likelihood estimation in latent variable models, the evidence lower bound (ELBO) produces state-of-the-art results. Inspired by this, we consider the extension of the ELBO to a family of lower bounds defined by a particle filter's estimator of the marginal likelihood, the filtering variational objectives (FIVOs). FIVOs take the same arguments as the ELBO, but can exploit a model's sequential structure to form tighter bounds. We present results that relate the tightness of FIVO's bound to the variance of the particle filter's estimator by considering the generic case of bounds defined as log-transformed likelihood estimators. Experimentally, we show that training with FIVO results in substantial improvements over training the same model architecture with the ELBO on sequential data.

Population activity measurement by calcium imaging can be combined with cellular resolution optogenetic activity perturbations to enable the mapping of neural connectivity in vivo. This requires accurate inference of perturbed and unperturbed neural activity from calcium imaging measurements, which are noisy and indirect, and can also be contaminated by photostimulation artifacts. We have developed a new fully Bayesian approach to jointly inferring spiking activity and neural connectivity from in vivo all-optical perturbation experiments. In contrast to standard approaches that perform spike inference and analysis in two separate maximum-likelihood phases, our joint model is able to propagate uncertainty in spike inference to the inference of connectivity and vice versa. We use the framework of variational autoencoders to model spiking activity using discrete latent variables, low-dimensional latent common input, and sparse spike-and-slab generalized linear coupling between neurons.

Random projections have been increasingly adopted for a diverse set of tasks in machine learning involving dimensionality reduction. One specific line of research on this topic has investigated the use of quantization subsequent to projection with the aim of additional data compression. Motivated by applications in nearest neighbor search and linear learning, we revisit the problem of recovering inner products (respectively cosine similarities) in such setting. We show that even under coarse scalar quantization with 3 to 5 bits per projection, the loss in accuracy tends to range from moderate''. One implication is that in most scenarios of practical interest, there is no need for a sophisticated recovery approach like maximum likelihood estimation as considered in previous work on the subject. What we propose herein also yields considerable improvements in terms of accuracy over the Hamming distance-based approach in Li et al. (ICML 2014) which is comparable in terms of simplicity

Many applications of machine learning, for example in health care, would benefit from methods that can guarantee privacy of data subjects. Differential privacy (DP) has become established as a standard for protecting learning results. The standard DP algorithms require a single trusted party to have access to the entire data, which is a clear weakness, or add prohibitive amounts of noise. We consider DP Bayesian learning in a distributed setting, where each party only holds a single sample or a few samples of the data. We propose a learning strategy based on a secure multi-party sum function for aggregating summaries from data holders and the Gaussian mechanism for DP. Our method builds on an asymptotically optimal and practically efficient DP Bayesian inference with rapidly diminishing extra cost.

We consider maximum likelihood estimation of linear dynamical systems with generalized-linear observation models. Maximum likelihood is typically considered to be hard in this setting since latent states and transition parameters must be inferred jointly. Given that expectation-maximization does not scale and is prone to local minima, moment-matching approaches from the subspace identification literature have become standard, despite known statistical efficiency issues. In this paper, we instead reconsider likelihood maximization and develop an optimization based strategy for recovering the latent states and transition parameters. Key to the approach is a two-view reformulation of maximum likelihood estimation for linear dynamical systems that enables the use of global optimization algorithms for matrix factorization. We show that the proposed estimation strategy outperforms widely-used identification algorithms such as subspace identification methods, both in terms of accuracy and runtime.

In sequential decision making, it is often important and useful for end users to understand the underlying patterns or causes that lead to the corresponding decisions. However, typical deep reinforcement learning algorithms seldom provide such information due to their black-box nature. In this paper, we present a probabilistic model, Q-LDA, to uncover latent patterns in text-based sequential decision processes. The model can be understood as a variant of latent topic models that are tailored to maximize total rewards; we further draw an interesting connection between an approximate maximum-likelihood estimation of Q-LDA and the celebrated Q-learning algorithm. We demonstrate in the text-game domain that our proposed method not only provides a viable mechanism to uncover latent patterns in decision processes, but also obtains state-of-the-art rewards in these games.

We explore the top-K rank aggregation problem in which one aims to recover a consistent ordering that focuses on top-K ranked items based on partially revealed preference information. We examine an M-wise comparison model that builds on the Plackett-Luce (PL) model where for each sample, M items are ranked according to their perceived utilities modeled as noisy observations of their underlying true utilities. As our result, we characterize the minimax optimality on the sample size for top-K ranking. The optimal sample size turns out to be inversely proportional to M. We devise an algorithm that effectively converts M-wise samples into pairwise ones and employs a spectral method using the refined data. In demonstrating its optimality, we develop a novel technique for deriving tight $\ell_\infty$ estimation error bounds, which is key to accurately analyzing the performance of top-K ranking algorithms, but has been challenging. Recent work relied on an additional maximum-likelihood estimation (MLE) stage merged with a spectral method to attain good estimates in $\ell_\infty$ error to achieve the limit for the pairwise model. In contrast, although it is valid in slightly restricted regimes, our result demonstrates a spectral method alone to be sufficient for the general M-wise model. We run numerical experiments using synthetic data and confirm that the optimal sample size decreases at the rate of 1/M. Moreover, running our algorithm on real-world data, we find that its applicability extends to settings that may not fit the PL model.

Decoding sensory stimuli from neural signals can be used to reveal how we sense our physical environment, and is valuable for the design of brain-machine interfaces. However, existing linear techniques for neural decoding may not fully reveal or exploit the fidelity of the neural signal. Here we develop a new approximate Bayesian method for decoding natural images from the spiking activity of populations of retinal ganglion cells (RGCs). We sidestep known computational challenges with Bayesian inference by exploiting artificial neural networks developed for computer vision, enabling fast nonlinear decoding that incorporates natural scene statistics implicitly. We use a decoder architecture that first linearly reconstructs an image from RGC spikes, then applies a convolutional autoencoder to enhance the image. The resulting decoder, trained on natural images and simulated neural responses, significantly outperforms linear decoding, as well as simple point-wise nonlinear decoding. These results provide a tool for the assessment and optimization of retinal prosthesis technologies, and reveal that the retina may provide a more accurate representation of the visual scene than previously appreciated.

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.

Predicated on the increasing abundance of electronic health records, we investigate the problem of inferring individualized treatment effects using observational data. Stemming from the potential outcomes model, we propose a novel multi-task learning framework in which factual and counterfactual outcomes are modeled as the outputs of a function in a vector-valued reproducing kernel Hilbert space (vvRKHS). We develop a nonparametric Bayesian method for learning the treatment effects using a multi-task Gaussian process (GP) with a linear coregionalization kernel as a prior over the vvRKHS. The Bayesian approach allows us to compute individualized measures of confidence in our estimates via pointwise credible intervals, which are crucial for realizing the full potential of precision medicine. The impact of selection bias is alleviated via a risk-based empirical Bayes method for adapting the multi-task GP prior, which jointly minimizes the empirical error in factual outcomes and the uncertainty in (unobserved) counterfactual outcomes. We conduct experiments on observational datasets for an interventional social program applied to premature infants, and a left ventricular assist device applied to cardiac patients wait-listed for a heart transplant. In both experiments, we show that our method significantly outperforms the state-of-the-art.