Flows based on either coupling or autoregressive transforms both offer exact density evaluation and sampling, but rely on the parameterization of an easily invertible elementwise transformation, whose choice determines the flexibility of these models. Building upon recent work, we propose a fully-differentiable module based on monotonic rational-quadratic splines, which enhances the flexibility of both coupling and autoregressive transforms while retaining analytic invertibility. We demonstrate that neural spline flows improve density estimation, variational inference, and generative modeling of images.

We consider the problem of functional matrix factorization, finding low-dimensional structure in a matrix where every entry is a noisy function evaluated at a set of discrete points. Such problems arise frequently in drug discovery, where biological samples form the rows, candidate drugs form the columns, and entries contain the dose-response curve of a sample treated at different concentrations of a drug. We propose Bayesian Tensor Filtering (BTF), a hierarchical Bayesian model of matrices of functions. BTF captures the smoothness in each individual function while also being locally adaptive to sharp discontinuities. The BTF model is agnostic to the likelihood of the underlying observations, making it flexible enough to handle many different kinds of data. We derive efficient Gibbs samplers for three classes of likelihoods: (i) Gaussian, for which updates are fully conjugate; (ii) Binomial and related likelihoods, for which updates are conditionally conjugate through P{\'o}lya--Gamma augmentation; and (iii) Black-box likelihoods, for which updates are non-conjugate but admit an analytic truncated elliptical slice sampling routine. We compare BTF against a state-of-the-art method for dynamic Poisson matrix factorization, showing BTF better reconstructs held out data in synthetic experiments. Finally, we build a dose-response model around BTF and show on real data from a multi-sample, multi-drug cancer study that BTF outperforms the current standard approach in biology. Code for BTF is available at https://github.com/tansey/functionalmf.

Estimating the effect of a treatment on a given outcome, conditioned on a vector of covariates, is central in many applications. However, learning the impact of a treatment on a continuous temporal response, when the covariates suffer extensively from measurement error and even the timing of the treatments is uncertain, has not been addressed. We introduce a novel data-driven method that can estimate treatment-response trajectories in this challenging scenario. We model personalized treatment-response curves as a combination of parametric response functions, hierarchically sharing information across individuals, and a sparse Gaussian process for the baseline trend. Importantly, our model considers measurement error not only in treatment covariates, but also in treatment times, a problem which arises in practice for example when treatment information is based on self-reporting. In a challenging and timely problem of estimating the impact of diet on continuous blood glucose measurements, our model leads to significant improvements in estimation accuracy and prediction.

Latent Euclidean embedding models a given network by representing each node in a Euclidean space, where the probability of two nodes sharing an edge is a function of the distances between the nodes. This implies that for two nodes to share an edge with high probability, they must be relatively close in all dimensions. This constraint may be overly restrictive for describing modern networks, in which having similarities in at least one area may be sufficient for having a high edge probability. We introduce a new model, which we call Latent Channel Networks, which allows for such features of a network. We present an EM algorithm for fitting the model, for which the computational complexity is linear in the number of edges and number of channels and apply the algorithm to both synthetic and classic network datasets.

Recent advances in variational inference enable the modelling of highly structured joint distributions, but are limited in their capacity to scale to the high-dimensional setting of stochastic neural networks. This limitation motivates a need for scalable parameterizations of the noise generation process, in a manner that adequately captures the dependencies among the various parameters. In this work, we address this need and present the Kronecker Flow, a generalization of the Kronecker product to invertible mappings designed for stochastic neural networks. We apply our method to variational Bayesian neural networks on predictive tasks, PAC-Bayes generalization bound estimation, and approximate Thompson sampling in contextual bandits. In all setups, our methods prove to be competitive with existing methods and better than the baselines.

We propose a new approach to address the text classification problems when learning with partial labels is beneficial. Instead of offering each training sample a set of candidate labels, we assign negative-oriented labels to the ambiguous training examples if they are unlikely fall into certain classes. We construct our new maximum likelihood estimators with self-correction property, and prove that under some conditions, our estimators converge faster. Also we discuss the advantages of applying one of our estimator to a fully supervised learning problem. The proposed method has potential applicability in many areas, such as crowdsourcing, natural language processing and medical image analysis.

In this note, we study the relationship between the variational gap and the variance of the (log) likelihood ratio. We show that the gap can be upper bounded by some form of dispersion measure of the likelihood ratio, which suggests the bias of variational inference can be reduced by making the distribution of the likelihood ratio more concentrated, such as via averaging and variance reduction.

One of the biggest challenges in robotics systems is interacting under uncertainty. Unlike robots, humans learn, adapt and perceive their body as a unity when interacting with the world. We hypothesize that the nervous system counteracts sensor and motor uncertainties by unconscious processes that robustly fuse the available information for approximating their body and the world state. Being able to unite perception and action under a common principle has been sought for decades and active inference is one of the potential unification theories. In this work, we present a humanoid robot interacting with the world by means of a human brain-like inspired perception and control algorithm based on the free-energy principle. Until now, active inference was only tested in simulated examples. Their application on a real robot shows the advantages of such an algorithm for real world applications. The humanoid robot iCub was capable of performing robust reaching behaviors with both arms and active head object tracking in the visual field, despite the visual noise, the artificially introduced noise in the joint encoders (up to 40 degrees deviation), the differences between the model and the real robot and the misdetections of the hand.

Gaussian Process Factor Analysis (GPFA) has been broadly applied to the problem of identifying smooth, low-dimensional temporal structure underlying large-scale neural recordings. However, spike trains are non-Gaussian, which motivates combining GPFA with discrete observation models for binned spike count data. The drawback to this approach is that GPFA priors are not conjugate to count model likelihoods, which makes inference challenging. Here we address this obstacle by introducing a fast, approximate inference method for non-conjugate GPFA models. Our approach uses orthogonal second-order polynomials to approximate the nonlinear terms in the non-conjugate log-likelihood, resulting in a method we refer to as polynomial approximate log-likelihood (PAL) estimators. This approximation allows for accurate closed-form evaluation of marginal likelihood and fast numerical optimization for parameters and hyperparameters. We derive PAL estimators for GPFA models with binomial, Poisson, and negative binomial observations, and additionally show that the parameters obtained can be used to initialize black-box variational inference, which significantly speeds up and stabilizes the inference procedure for these factor analytic models. We apply these methods to data from mouse visual cortex and monkey higher-order visual and parietal cortices, and compare GPFA under three different spike count observation models to traditional GPFA. We demonstrate that PAL estimators achieve fast and accurate extraction of latent structure from multi-neuron spike train data.

One-Shot Neural Architecture Search (NAS) is a promising method to significantly reduce search time without any separate training. It can be treated as a Network Compression problem on the architecture parameters from an over-parameterized network. However, there are two issues associated with most one-shot NAS methods. First, dependencies between a node and its predecessors and successors are often disregarded which result in improper treatment over zero operations. Second, architecture parameters pruning based on their magnitude is questionable. In this paper, we employ the classic Bayesian learning approach to alleviate these two issues by modeling architecture parameters using hierarchical automatic relevance determination (HARD) priors. Unlike other NAS methods, we train the over-parameterized network for only one epoch then update the architecture. Impressively, this enabled us to find the architecture on CIFAR-10 within only 0.2 GPU days using a single GPU. Competitive performance can be also achieved by transferring to ImageNet. As a byproduct, our approach can be applied directly to compress convolutional neural networks by enforcing structural sparsity which achieves extremely sparse networks without accuracy deterioration.