We study the implementation of Automatic Differentiation Variational inference (ADVI) for Bayesian inference on regression models with bridge penalization. The bridge approach uses $\ell_{\alpha}$ norm, with $\alpha \in (0, +\infty)$ to define a penalization on large values of the regression coefficients, which includes the Lasso ($\alpha = 1$) and ridge $(\alpha = 2)$ penalizations as special cases. Full Bayesian inference seamlessly provides joint uncertainty estimates for all model parameters. Although MCMC aproaches are available for bridge regression, it can be slow for large dataset, specially in high dimensions. The ADVI implementation allows the use of small batches of data at each iteration (due to stochastic gradient based algorithms), therefore speeding up computational time in comparison with MCMC. We illustrate the approach on non-parametric regression models with B-splines, although the method works seamlessly for other choices of basis functions. A simulation study shows the main properties of the proposed method.
Probabilistic programs provide an expressive representation language for generative models. Given a probabilistic program, we are interested in the task of posterior inference: estimating a latent variable given a set of observed variables. Existing techniques for inference in probabilistic programs often require choosing many hyper-parameters, are computationally expensive, and/or only work for restricted classes of programs. Here we formulate inference as masked language modeling: given a program, we generate a supervised dataset of variables and assignments, and randomly mask a subset of the assignments. We then train a neural network to unmask the random values, defining an approximate posterior distribution. By optimizing a single neural network across a range of programs we amortize the cost of training, yielding a "foundation" posterior able to do zero-shot inference for new programs. The foundation posterior can also be fine-tuned for a particular program and dataset by optimizing a variational inference objective. We show the efficacy of the approach, zero-shot and fine-tuned, on a benchmark of STAN programs.
Switching dynamical systems are an expressive model class for the analysis of time-series data. As in many fields within the natural and engineering sciences, the systems under study typically evolve continuously in time, it is natural to consider continuous-time model formulations consisting of switching stochastic differential equations governed by an underlying Markov jump process. Inference in these types of models is however notoriously difficult, and tractable computational schemes are rare. In this work, we propose a novel inference algorithm utilizing a Markov Chain Monte Carlo approach. The presented Gibbs sampler allows to efficiently obtain samples from the exact continuous-time posterior processes. Our framework naturally enables Bayesian parameter estimation, and we also include an estimate for the diffusion covariance, which is oftentimes assumed fixed in stochastic differential equation models. We evaluate our framework under the modeling assumption and compare it against an existing variational inference approach.
While fat-tailed densities commonly arise as posterior and marginal distributions in robust models and scale mixtures, they present challenges when Gaussian-based variational inference fails to capture tail decay accurately. We first improve previous theory on tails of Lipschitz flows by quantifying how the tails affect the rate of tail decay and by expanding the theory to non-Lipschitz polynomial flows. Then, we develop an alternative theory for multivariate tail parameters which is sensitive to tail-anisotropy. In doing so, we unveil a fundamental problem which plagues many existing flow-based methods: they can only model tail-isotropic distributions (i.e., distributions having the same tail parameter in every direction). To mitigate this and enable modeling of tail-anisotropic targets, we propose anisotropic tail-adaptive flows (ATAF). Experimental results on both synthetic and real-world targets confirm that ATAF is competitive with prior work while also exhibiting appropriate tail-anisotropy.
Utilizing amortized variational inference for latent-action reinforcement learning (RL) has been shown to be an effective approach in Task-oriented Dialogue (ToD) systems for optimizing dialogue success. Until now, categorical posteriors have been argued to be one of the main drivers of performance. In this work we revisit Gaussian variational posteriors for latent-action RL and show that they can yield even better performance than categoricals. We achieve this by simplifying the training procedure and propose ways to regularize the latent dialogue policy to retain good response coherence. Using continuous latent representations our model achieves state of the art dialogue success rate on the MultiWOZ benchmark, and also compares well to categorical latent methods in response coherence.
This work presents mixed variational flows (MixFlows), a new variational family that consists of a mixture of repeated applications of a map to an initial reference distribution. First, we provide efficient algorithms for i.i.d. sampling, density evaluation, and unbiased ELBO estimation. We then show that MixFlows have MCMC-like convergence guarantees when the flow map is ergodic and measure-preserving, and provide bounds on the accumulation of error for practical implementations where the flow map is approximated. Finally, we develop an implementation of MixFlows based on uncorrected discretized Hamiltonian dynamics combined with deterministic momentum refreshment. Simulated and real data experiments show that MixFlows can provide more reliable posterior approximations than several black-box normalizing flows, as well as samples of comparable quality to those obtained from state-of-the-art MCMC methods.
Scene graph generation is a structured prediction task aiming to explicitly model objects and their relationships via constructing a visually-grounded scene graph for an input image. Currently, the message passing neural network based mean field variational Bayesian methodology is the ubiquitous solution for such a task, in which the variational inference objective is often assumed to be the classical evidence lower bound. However, the variational approximation inferred from such loose objective generally underestimates the underlying posterior, which often leads to inferior generation performance. In this paper, we propose a novel importance weighted structure learning method aiming to approximate the underlying log-partition function with a tighter importance weighted lower bound, which is computed from multiple samples drawn from a reparameterizable Gumbel-Softmax sampler. A generic entropic mirror descent algorithm is applied to solve the resulting constrained variational inference task. The proposed method achieves the state-of-the-art performance on various popular scene graph generation benchmarks.
Cross-Domain Recommendation (CDR) has been popularly studied to utilize different domain knowledge to solve the cold-start problem in recommender systems. Most of the existing CDR models assume that both the source and target domains share the same overlapped user set for knowledge transfer. However, only few proportion of users simultaneously activate on both the source and target domains in practical CDR tasks. In this paper, we focus on the Partially Overlapped Cross-Domain Recommendation (POCDR) problem, that is, how to leverage the information of both the overlapped and non-overlapped users to improve recommendation performance. Existing approaches cannot fully utilize the useful knowledge behind the non-overlapped users across domains, which limits the model performance when the majority of users turn out to be non-overlapped. To address this issue, we propose an end-to-end dual-autoencoder with Variational Domain-invariant Embedding Alignment (VDEA) model, a cross-domain recommendation framework for the POCDR problem, which utilizes dual variational autoencoders with both local and global embedding alignment for exploiting domain-invariant user embedding. VDEA first adopts variational inference to capture collaborative user preferences, and then utilizes Gromov-Wasserstein distribution co-clustering optimal transport to cluster the users with similar rating interaction behaviors. Our empirical studies on Douban and Amazon datasets demonstrate that VDEA significantly outperforms the state-of-the-art models, especially under the POCDR setting.
We develop a framework for generalized variational inference in infinite-dimensional function spaces and use it to construct a method termed Gaussian Wasserstein inference (GWI). GWI leverages the Wasserstein distance between Gaussian measures on the Hilbert space of square-integrable functions in order to determine a variational posterior using a tractable optimisation criterion and avoids pathologies arising in standard variational function space inference. An exciting application of GWI is the ability to use deep neural networks in the variational parametrisation of GWI, combining their superior predictive performance with the principled uncertainty quantification analogous to that of Gaussian processes. The proposed method obtains state-of-the-art performance on several benchmark datasets.
Parametric verification of linear temporal properties for stochastic models can be expressed as computing the satisfaction probability of a certain property as a function of the parameters of the model. Smoothed model checking (smMC) aims at inferring the satisfaction function over the entire parameter space from a limited set of observations obtained via simulation. As observations are costly and noisy, smMC is framed as a Bayesian inference problem so that the estimates have an additional quantification of the uncertainty. In smMC the authors use Gaussian Processes (GP), inferred by means of the Expectation Propagation algorithm. This approach provides accurate reconstructions with statistically sound quantification of the uncertainty. However, it inherits the well-known scalability issues of GP. In this paper, we exploit recent advances in probabilistic machine learning to push this limitation forward, making Bayesian inference of smMC scalable to larger datasets and enabling its application to models with high dimensional parameter spaces. We propose Stochastic Variational Smoothed Model Checking (SV-smMC), a solution that exploits stochastic variational inference (SVI) to approximate the posterior distribution of the smMC problem. The strength and flexibility of SVI make SV-smMC applicable to two alternative probabilistic models: Gaussian Processes (GP) and Bayesian Neural Networks (BNN). The core ingredient of SVI is a stochastic gradient-based optimization that makes inference easily parallelizable and that enables GPU acceleration. In this paper, we compare the performances of smMC against those of SV-smMC by looking at the scalability, the computational efficiency and the accuracy of the reconstructed satisfaction function.
We propose a Model Predictive Control (MPC) method for collision-free navigation that uses amortized variational inference to approximate the distribution of optimal control sequences by training a normalizing flow conditioned on the start, goal and environment. This representation allows us to learn a distribution that accounts for both the dynamics of the robot and complex obstacle geometries. We can then sample from this distribution to produce control sequences which are likely to be both goal-directed and collision-free as part of our proposed FlowMPPI sampling-based MPC method. However, when deploying this method, the robot may encounter an out-of-distribution (OOD) environment, i.e. one which is radically different from those used in training. In such cases, the learned flow cannot be trusted to produce low-cost control sequences. To generalize our method to OOD environments we also present an approach that performs projection on the representation of the environment as part of the MPC process. This projection changes the environment representation to be more in-distribution while also optimizing trajectory quality in the true environment. Our simulation results on a 2D double-integrator and a 3D 12DoF underactuated quadrotor suggest that FlowMPPI with projection outperforms state-of-the-art MPC baselines on both in-distribution and OOD environments, including OOD environments generated from real-world data.
We propose a simultaneous learning and pruning algorithm capable of identifying and eliminating irrelevant structures in a neural network during the early stages of training. Thus, the computational cost of subsequent training iterations, besides that of inference, is considerably reduced. Our method, based on variational inference principles using Gaussian scale mixture priors on neural network weights, learns the variational posterior distribution of Bernoulli random variables multiplying the units/filters similarly to adaptive dropout. Our algorithm, ensures that the Bernoulli parameters practically converge to either 0 or 1, establishing a deterministic final network. We analytically derive a novel hyper-prior distribution over the prior parameters that is crucial for their optimal selection and leads to consistent pruning levels and prediction accuracy regardless of weight initialization or the size of the starting network. We prove the convergence properties of our algorithm establishing theoretical and practical pruning conditions. We evaluate the proposed algorithm on the MNIST and CIFAR-10 data sets and the commonly used fully connected and convolutional LeNet and VGG16 architectures. The simulations show that our method achieves pruning levels on par with state-of the-art methods for structured pruning, while maintaining better test-accuracy and more importantly in a manner robust with respect to network initialization and initial size.
Applied category theory has recently developed libraries for computing with morphisms in interesting categories, while machine learning has developed ways of learning programs in interesting languages. Taking the analogy between categories and languages seriously, this paper defines a probabilistic generative model of morphisms in free monoidal categories over domain-specific generating objects and morphisms. The paper shows how acyclic directed wiring diagrams can model specifications for morphisms, which the model can use to generate morphisms. Amortized variational inference in the generative model then enables learning of parameters (by maximum likelihood) and inference of latent variables (by Bayesian inversion). A concrete experiment shows that the free category prior achieves competitive reconstruction performance on the Omniglot dataset.
Controlling the environmental parameters, including light in greenhouses, increases the crop yield; however, the electricity cost of supplemental lighting can be high. Therefore, the importance of applying cost-effective lighting methods arises. In this paper, an optimal supplemental lighting control approach is developed considering a variational inference Bayesian Neural Network (BNN) model for sunlight prediction. The predictive model is validated through testing the model on the historical solar data of a site located at North Carolina ($R^{2}$=0.9971, RMSE=1.8%). The proposed lighting approach is shown to minimize electricity cost by considering the BNN-based sunlight prediction, plant light needs, and variable electricity pricing when solving the underlying optimization problem. For evaluation, the new strategy is compared to: 1) a Markov-based prediction method, which solves the same optimization problem, assuming a Markov model for sunlight prediction; 2) a heuristic method which aims to supply a fixed amount of light. Simulation studies are conducted to examine the electricity cost improvements of the BNN-based approach. The results show that the BNN-based approach reduces cost by (on average) 2.27% and 43.91% compared to the Markov prediction-based method and the heuristic method, respectively, throughout a year.
Sparse coding strategies have been lauded for their parsimonious representations of data that leverage low dimensional structure. However, inference of these codes typically relies on an optimization procedure with poor computational scaling in high-dimensional problems. For example, sparse inference in the representations learned in the high-dimensional intermediary layers of deep neural networks (DNNs) requires an iterative minimization to be performed at each training step. As such, recent, quick methods in variational inference have been proposed to infer sparse codes by learning a distribution over the codes with a DNN. In this work, we propose a new approach to variational sparse coding that allows us to learn sparse distributions by thresholding samples, avoiding the use of problematic relaxations. We first evaluate and analyze our method by training a linear generator, showing that it has superior performance, statistical efficiency, and gradient estimation compared to other sparse distributions. We then compare to a standard variational autoencoder using a DNN generator on the Fashion MNIST and CelebA datasets
The Gumbel-softmax distribution, or Concrete distribution, is often used to relax the discrete characteristics of a categorical distribution and enable back-propagation through differentiable reparameterization. Although it reliably yields low variance gradients, it still relies on a stochastic sampling process for optimization. In this work, we present a relaxed categorical analytic bound (ReCAB), a novel divergence-like metric which corresponds to the upper bound of the Kullback-Leibler divergence (KLD) of a relaxed categorical distribution. The proposed metric is easy to implement because it has a closed form solution, and empirical results show that it is close to the actual KLD. Along with this new metric, we propose a relaxed categorical analytic bound variational autoencoder (ReCAB-VAE) that successfully models both continuous and relaxed discrete latent representations. We implement an emotional text-to-speech synthesis system based on the proposed framework, and show that the proposed system flexibly and stably controls emotion expressions with better speech quality compared to baselines that use stochastic estimation or categorical distribution approximation.
Probabilistic control design is founded on the principle that a rational agent attempts to match modelled with an arbitrary desired closed-loop system trajectory density. The framework was originally proposed as a tractable alternative to traditional optimal control design, parametrizing desired behaviour through fictitious transition and policy densities and using the information projection as a proximity measure. In this work we introduce an alternative parametrization of desired closed-loop behaviour and explore alternative proximity measures between densities. It is then illustrated how the associated probabilistic control problems solve into uncertain or probabilistic policies. Our main result is to show that the probabilistic control objectives majorize conventional, stochastic and risk sensitive, optimal control objectives. This observation allows us to identify two probabilistic fixed point iterations that converge to the deterministic optimal control policies establishing an explicit connection between either formulations. Further we demonstrate that the risk sensitive optimal control formulation is also technically equivalent to a Maximum Likelihood estimation problem on a probabilistic graph model where the notion of costs is directly encoded into the model. The associated treatment of the estimation problem is then shown to coincide with the moment projected probabilistic control formulation. That way optimal decision making can be reformulated as an iterative inference problem. Based on these insights we discuss directions for algorithmic development.
Object tracking is one of the fundamental problems in visual recognition tasks and has achieved significant improvements in recent years. The achievements often come with the price of enormous hardware consumption and expensive labor effort for consecutive labeling. A missing ingredient for robust tracking is achieving performance with minimal modification on network structure and semi-supervised learning intermittent labeled frames. In this paper, we ad-dress these problems in a Bayesian tracking and detection framework parameterized by neural network outputs. In our framework, the tracking and detection process is formulated in a probabilistic way as multi-objects dynamics and network detection uncertainties. With our formulation, we propose a particle filter-based approximate sampling algorithm for tracking object state estimation. Based on our particle filter inference algorithm, a semi-supervised learn-ing algorithm is utilized for learning tracking network on intermittent labeled frames by variational inference. In our experiments, we provide both mAP and probability-based detection measurements for comparison between our algorithm with non-Bayesian solutions. We also train a semi-supervised tracking network on M2Cai16-Tool-Locations Dataset and compare our results with supervised learning on fully labeled frames.
Learning from a continuous stream of non-stationary data in an unsupervised manner is arguably one of the most common and most challenging settings facing intelligent agents. Here, we attack learning under all three conditions (unsupervised, streaming, non-stationary) in the context of clustering, also known as mixture modeling. We introduce a novel clustering algorithm that endows mixture models with the ability to create new clusters online, as demanded by the data, in a probabilistic, time-varying, and principled manner. To achieve this, we first define a novel stochastic process called the Dynamical Chinese Restaurant Process (Dynamical CRP), which is a non-exchangeable distribution over partitions of a set; next, we show that the Dynamical CRP provides a non-stationary prior over cluster assignments and yields an efficient streaming variational inference algorithm. We conclude with experiments showing that the Dynamical CRP can be applied on diverse synthetic and real data with Gaussian and non-Gaussian likelihoods.
A central goal in the cognitive sciences is the development of numerical models for mental representations of object concepts. This paper introduces Variational Interpretable Concept Embeddings (VICE), an approximate Bayesian method for embedding object concepts in a vector space using data collected from humans in a triplet odd-one-out task. VICE uses variational inference to obtain sparse, non-negative representations of object concepts with uncertainty estimates for the embedding values. These estimates are used to automatically select the dimensions that best explain the data. We derive a PAC learning bound for VICE that can be used to estimate generalization performance or determine a sufficient sample size for experimental design. VICE rivals or outperforms its predecessor, SPoSE, at predicting human behavior in the triplet odd-one-out task. Furthermore, VICE's object representations are more reproducible and consistent across random initializations, highlighting the unique advantage of using VICE for deriving interpretable embeddings from human behavior.