Bayesian Inference
Variationally Inferred Sampling Through a Refined Bound for Probabilistic Programs
Gallego, Victor, Insua, David Rios
A framework to boost efficiency of Bayesian inference in probabilistic programs is introduced by embedding a sampler inside a variational posterior approximation, which we call the refined variational approximation. Its strength lies both in ease of implementation and in automatically tuning the sampler parameters to speed up mixing time. Several strategies to approximate the \emph{evidence lower bound} (ELBO) computation are introduced, including a rewriting of the ELBO objective. A specialization towards state-space models is proposed. Experimental evidence of its efficient performance is shown by solving an influence diagram in a high-dimensional space using a conditional variational autoencoder (cVAE) as a deep Bayes classifier; an unconditional VAE on density estimation tasks; and state-space models for time-series data.
Compiling Stochastic Constraint Programs to And-Or Decision Diagrams
Babaki, Behrouz, Farnadi, Golnoosh, Pesant, Gilles
Factored stochastic constraint programming (FSCP) is a formalism to represent multi-stage decision making problems under uncertainty. FSCP models support factorized probabilistic models and involve constraints over decision and random variables. These models have many applications in real-world problems. However, solving these problems requires evaluating the best course of action for each possible outcome of the random variables and hence is computationally challenging. FSCP problems often involve repeated subproblems which ideally should be solved once. In this paper we show how identifying and exploiting these identical subproblems can simplify solving them and leads to a compact representation of the solution. We compile an And-Or search tree to a compact decision diagram. Preliminary experiments show that our proposed method significantly improves the search efficiency by reducing the size of the problem and outperforms the existing methods.
Satisficing Mentalizing: Bayesian Models of Theory of Mind Reasoning in Scenarios with Different Uncertainties
The ability to interpret the mental state of another agent based on its behavior, also called Theory of Mind (ToM), is crucial for humans in any kind of social interaction. Artificial systems, such as intelligent assistants, would also greatly benefit from such mentalizing capabilities. However, humans and systems alike are bound by limitations in their available computational resources. This raises the need for satisficing mentalizing, reconciling accuracy and efficiency in mental state inference that is good enough for a given situation. In this paper, we present different Bayesian models of ToM reasoning and evaluate them based on actual human behavior data that were generated under different kinds of uncertainties. We propose a Switching approach that combines specialized models, embodying simplifying presumptions, in order to achieve a more statisficing mentalizing compared to a Full Bayesian ToM model.
Can A User Anticipate What Her Followers Want?
De, Abir, Singla, Adish, Upadhyay, Utkarsh, Gomez-Rodriguez, Manuel
Whenever a social media user decides to share a story, she is typically pleased to receive likes, comments, shares, or, more generally, feedback from her followers. As a result, she may feel compelled to use the feedback she receives to (re-)estimate her followers' preferences and decides which stories to share next to receive more (positive) feedback. Under which conditions can she succeed? In this work, we first look into this problem from a theoretical perspective and then provide a set of practical algorithms to identify and characterize such behavior in social media. More specifically, we address the above problem from the viewpoint of sequential decision making and utility maximization. For a wide variety of utility functions, we first show that, to succeed, a user needs to actively trade off exploitation-- sharing stories which lead to more (positive) feedback--and exploration-- sharing stories to learn about her followers' preferences. However, exploration is not necessary if a user utilizes the feedback her followers provide to other users in addition to the feedback she receives. Then, we develop a utility estimation framework for observation data, which relies on statistical hypothesis testing to determine whether a user utilizes the feedback she receives from each of her followers to decide what to post next. Experiments on synthetic data illustrate our theoretical findings and show that our estimation framework is able to accurately recover users' underlying utility functions. Experiments on several real datasets gathered from Twitter and Reddit reveal that up to 82% (43%) of the Twitter (Reddit) users in our datasets do use the feedback they receive to decide what to post next.
Adversarial $\alpha$-divergence Minimization for Bayesian Approximate Inference
Santana, Simón Rodríguez, Hernández-Lobato, Daniel
Neural networks are popular models for regression. They are often trained via back-propagation to find a value of the weights that correctly predicts the observed data. Although back-propagation has shown good performance in many applications, it cannot easily output an estimate of the uncertainty in the predictions made. Measuring this uncertainty in the predictions of machine learning models is a critical aspect with important applications. Uncertainty estimates can be obtained by following a Bayesian approach in which a posterior distribution of the model parameters is computed. The posterior distribution summarizes which parameter values are compatible with the data. Typically,this posterior distribution is intractable and has to be approximated. Several approaches have been considered for solving this problem. We propose here a general method for approximate Bayesian inference based on minimizing{\alpha}-divergences which allows for flexible approximate distributions. The method is evaluated in the context of Bayesian neural networks for regression on extensive experiments. The results show that it often gives better performance in terms of the test log-likelihood and sometimes in terms of the squared error.
Hierarchical Reinforcement Learning for Open-Domain Dialog
Saleh, Abdelrhman, Jaques, Natasha, Ghandeharioun, Asma, Shen, Judy Hanwen, Picard, Rosalind
Open-domain dialog generation is a challenging problem; maximum likelihood training can lead to repetitive outputs, models have difficulty tracking long-term conversational goals, and training on standard movie or online datasets may lead to the generation of inappropriate, biased, or offensive text. Reinforcement Learning (RL) is a powerful framework that could potentially address these issues, for example by allowing a dialog model to optimize for reducing toxicity and repetitiveness. However, previous approaches which apply RL to open-domain dialog generation do so at the word level, making it difficult for the model to learn proper credit assignment for long-term conversational rewards. In this paper, we propose a novel approach to hierarchical reinforcement learning, VHRL, which uses policy gradients to tune the utterance-level embedding of a variational sequence model. This hierarchical approach provides greater flexibility for learning long-term, conversational rewards. We use self-play and RL to optimize for a set of human-centered conversation metrics, and show that our approach provides significant improvements -- in terms of both human evaluation and automatic metrics -- over state-of-the-art dialog models, including Transformers.
Unsupervised Segmentation of Fire and Smoke from Infra-Red Videos
Ajith, Meenu, Martínez-Ramón, Manel
This paper proposes a vision-based fire and smoke segmentation system which use spatial, temporal and motion information to extract the desired regions from the video frames. The fusion of information is done using multiple features such as optical flow, divergence and intensity values. These features extracted from the images are used to segment the pixels into different classes in an unsupervised way. A comparative analysis is done by using multiple clustering algorithms for segmentation. Here the Markov Random Field performs more accurately than other segmentation algorithms since it characterizes the spatial interactions of pixels using a finite number of parameters. It builds a probabilistic image model that selects the most likely labeling using the maximum a posteriori (MAP) estimation. This unsupervised approach is tested on various images and achieves a frame-wise fire detection rate of 95.39%. Hence this method can be used for early detection of fire in real-time and it can be incorporated into an indoor or outdoor surveillance system.
Towards a New Understanding of the Training of Neural Networks with Mislabeled Training Data
Gish, Herbert, Silovsky, Jan, Sung, Man-Ling, Siu, Man-Hung, Hartmann, William, Jiang, Zhuolin
We investigate the problem of machine learning with mislabeled training data. We try to make the effects of mislabeled training better understood through analysis of the basic model and equations that characterize the problem. This includes results about the ability of the noisy model to make the same decisions as the clean model and the effects of noise on model performance. In addition to providing better insights we also are able to show that the Maximum Likelihood (ML) estimate of the parameters of the noisy model determine those of the clean model. This property is obtained through the use of the ML invariance property and leads to an approach to developing a classifier when training has been mislabeled: namely train the classifier on noisy data and adjust the decision threshold based on the noise levels and/or class priors. We show how our approach to mislabeled training works with multi-layered perceptrons (MLPs).
Knowledge representation and diagnostic inference using Bayesian networks in the medical discourse
Flügge, Sebastian, Zimmer, Sandra, Petersohn, Uwe
For the diagnostic inference under uncertainty Bayesian networks are investigated. The method is based on an adequate uniform representation of the necessary knowledge. This includes both generic and experience-based specific knowledge, which is stored in a knowledge base. For knowledge processing, a combination of the problem-solving methods of concept-based and case-based reasoning is used. Concept-based reasoning is used for the diagnosis, therapy and medication recommendation and evaluation of generic knowledge. Exceptions in the form of specific patient cases are processed by case-based reasoning. In addition, the use of Bayesian networks allows to deal with uncertainty, fuzziness and incompleteness. Thus, the valid general concepts can be issued according to their probability. To this end, various inference mechanisms are introduced and subsequently evaluated within the context of a developed prototype. Tests are employed to assess the classification of diagnoses by the network.