Bayesian Learning
Classical Planning in Deep Latent Space
Asai, Masataro | Kajino, Hiroshi (IBM Research - Tokyo, Tokyo Japan) | Fukunaga, Alex (Graduate School of Arts and Sciences, University of Tokyo, Tokyo Japan) | Muise, Christian (School of Computing, Queenโs University, Kingston Canada)
Current domain-independent, classical planners require symbolic models of the problem domain and instance as input, resulting in a knowledge acquisition bottleneck. Meanwhile, although deep learning has achieved significant success in many fields, the knowledge is encoded in a subsymbolic representation which is incompatible with symbolic systems such as planners. We propose Latplan, an unsupervised architecture combining deep learning and classical planning. Given only an unlabeled set of image pairs showing a subset of transitions allowed in the environment (training inputs), Latplan learns a complete propositional PDDL action model of the environment. Later, when a pair of images representing the initial and the goal states (planning inputs) is given, Latplan finds a plan to the goal state in a symbolic latent space and returns a visualized plan execution. We evaluate Latplan using image-based versions of 6 planning domains: 8-puzzle, 15-Puzzle, Blocksworld, Sokoban and Two variations of LightsOut.
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Sparse Representation Learning with Modified q-VAE towards Minimal Realization of World Model
Kobayashi, Taisuke, Watanuki, Ryoma
Extraction of low-dimensional latent space from high-dimensional observation data is essential to construct a real-time robot controller with a world model on the extracted latent space. However, there is no established method for tuning the dimension size of the latent space automatically, suffering from finding the necessary and sufficient dimension size, i.e. the minimal realization of the world model. In this study, we analyze and improve Tsallis-based variational autoencoder (q-VAE), and reveal that, under an appropriate configuration, it always facilitates making the latent space sparse. Even if the dimension size of the pre-specified latent space is redundant compared to the minimal realization, this sparsification collapses unnecessary dimensions, allowing for easy removal of them. We experimentally verified the benefits of the sparsification by the proposed method that it can easily find the necessary and sufficient six dimensions for a reaching task with a mobile manipulator that requires a six-dimensional state space. Moreover, by planning with such a minimal-realization world model learned in the extracted dimensions, the proposed method was able to exert a more optimal action sequence in real-time, reducing the reaching accomplishment time by around 20 %. The attached video is uploaded on youtube: https://youtu.be/-QjITrnxaRs
Correcting Model Bias with Sparse Implicit Processes
Santana, Simรณn Rodrรญguez, Ortega, Luis A., Hernรกndez-Lobato, Daniel, Zaldรญvar, Bryan
Model selection in machine learning (ML) is a crucial part of the Bayesian learning procedure. Model choice may impose strong biases on the resulting predictions, which can hinder the performance of methods such as Bayesian neural networks and neural samplers. On the other hand, newly proposed approaches for Bayesian ML exploit features of approximate inference in function space with implicit stochastic processes (a generalization of Gaussian processes). The approach of Sparse Implicit Processes (SIP) is particularly successful in this regard, since it is fully trainable and achieves flexible predictions. Here, we expand on the original experiments to show that SIP is capable of correcting model bias when the data generating mechanism differs strongly from the one implied by the model. We use synthetic datasets to show that SIP is capable of providing predictive distributions that reflect the data better than the exact predictions of the initial, but wrongly assumed model.
Uncertain Bayesian Networks: Learning from Incomplete Data
Hougen, Conrad D., Kaplan, Lance M., Cerutti, Federico, Hero, Alfred O. III
When the historical data are limited, the conditional probabilities associated with the nodes of Bayesian networks are uncertain and can be empirically estimated. Second order estimation methods provide a framework for both estimating the probabilities and quantifying the uncertainty in these estimates. We refer to these cases as uncer tain or second-order Bayesian networks. When such data are complete, i.e., all variable values are observed for each instantiation, the conditional probabilities are known to be Dirichlet-distributed. This paper improves the current state-of-the-art approaches for handling uncertain Bayesian networks by enabling them to learn distributions for their parameters, i.e., conditional probabilities, with incomplete data. We extensively evaluate various methods to learn the posterior of the parameters through the desired and empirically derived strength of confidence bounds for various queries.
Channel Estimation under Hardware Impairments: Bayesian Methods versus Deep Learning
Demir, รzlem Tugfe, Bjรถrnson, Emil
This paper considers the impact of general hardware impairments in a multiple-antenna base station and user equipments on the uplink performance. First, the effective channels are analytically derived for distortion-aware receivers when using finite-sized signal constellations. Next, a deep feedforward neural network is designed and trained to estimate the effective channels. Its performance is compared with state-of-the-art distortion-aware and unaware Bayesian linear minimum mean-squared error (LMMSE) estimators. The proposed deep learning approach improves the estimation quality by exploiting impairment characteristics, while LMMSE methods treat distortion as noise.
A Parallel Technique for Multi-objective Bayesian Global Optimization: Using a Batch Selection of Probability of Improvement
Yang, Kaifeng, Dong, Guozhi, Affenzeller, Michael
Bayesian global optimization (BGO) is an efficient surrogate-assisted technique for problems involving expensive evaluations. A parallel technique can be used to parallelly evaluate the true-expensive objective functions in one iteration to boost the execution time. An effective and straightforward approach is to design an acquisition function that can evaluate the performance of a bath of multiple solutions, instead of a single point/solution, in one iteration. This paper proposes five alternatives of \emph{Probability of Improvement} (PoI) with multiple points in a batch (q-PoI) for multi-objective Bayesian global optimization (MOBGO), taking the covariance among multiple points into account. Both exact computational formulas and the Monte Carlo approximation algorithms for all proposed q-PoIs are provided. Based on the distribution of the multiple points relevant to the Pareto-front, the position-dependent behavior of the five q-PoIs is investigated. Moreover, the five q-PoIs are compared with the other nine state-of-the-art and recently proposed batch MOBGO algorithms on twenty bio-objective benchmarks. The empirical experiments on different variety of benchmarks are conducted to demonstrate the effectiveness of two greedy q-PoIs ($\kpoi_{\mbox{best}}$ and $\kpoi_{\mbox{all}}$) on low-dimensional problems and the effectiveness of two explorative q-PoIs ($\kpoi_{\mbox{one}}$ and $\kpoi_{\mbox{worst}}$) on high-dimensional problems with difficult-to-approximate Pareto front boundaries.
Transmission Neural Networks: From Virus Spread Models to Neural Networks
This work connects models for virus spread on networks with their equivalent neural network representations. Based on this connection, we propose a new neural network architecture, called Transmission Neural Networks (TransNNs) where activation functions are primarily associated with links and are allowed to have different activation levels. Furthermore, this connection leads to the discovery and the derivation of three new activation functions with tunable or trainable parameters. Moreover, we prove that TransNNs with a single hidden layer and a fixed non-zero bias term are universal function approximators. Finally, we present new fundamental derivations of continuous time epidemic network models based on TransNNs.
Bayesian predictive modeling of multi-source multi-way data
Kim, Jonathan, Sandri, Brian J., Rao, Raghavendra B., Lock, Eric F.
We develop a Bayesian approach to predict a continuous or binary outcome from data that are collected from multiple sources with a multi-way (i.e.. multidimensional tensor) structure. As a motivating example we consider molecular data from multiple 'omics sources, each measured over multiple developmental time points, as predictors of early-life iron deficiency (ID) in a rhesus monkey model. We use a linear model with a low-rank structure on the coefficients to capture multi-way dependence and model the variance of the coefficients separately across each source to infer their relative contributions. Conjugate priors facilitate an efficient Gibbs sampling algorithm for posterior inference, assuming a continuous outcome with normal errors or a binary outcome with a probit link. Simulations demonstrate that our model performs as expected in terms of misclassification rates and correlation of estimated coefficients with true coefficients, with large gains in performance by incorporating multi-way structure and modest gains when accounting for differing signal sizes across the different sources. Moreover, it provides robust classification of ID monkeys for our motivating application. Software in the form of R code is available at https://github.com/BiostatsKim/BayesMSMW .
Motivating explanations in Bayesian networks using MAP-independence
Motivating explanations in Bayesian networks using MAP-independence Johan Kwisthout We introduce MAP-independence as a novel concept in Bayesian networks, indicating potential impact of an intermediate (hidden) variable to the MAP explanation. We discuss how this concept may contribute to justifying MAP explanations, for example in the context of a decision support system. Abstract In decision support systems the motivation and justification of the system's diagnosis or classification is crucial for the acceptance of the system by the human user. In Bayesian networks a diagnosis or classification is typically formalized as the computation of the most probable joint value assignment to the hypothesis variables, given the observed values of the evidence variables (generally known as the MAP problem). While solving the MAP problem gives the most probable explanation of the evidence, the computation is a black box as far as the human user is concerned and it does not give additional insights that allow the user to appreciate and accept the decision. For example, a user might want to know to whether an unobserved variable could potentially (upon observation) impact the explanation, or whether it is irrelevant in this aspect.