A Tutorial on Bayesian Nonparametric Models

A key problem in statistical modeling is model selection, how to choose a model at an appropriate level of complexity. This problem appears in many settings, most prominently in choosing the number ofclusters in mixture models or the number of factors in factor analysis. In this tutorial we describe Bayesian nonparametric methods, a class of methods that side-steps this issue by allowing the data to determine the complexity of the model. This tutorial is a high-level introduction to Bayesian nonparametric methods and contains several examples of their application.Comment: 28 pages, 8 figure

What does the free energy principle tell us about the brain?

The free energy principle has been proposed as a unifying account of brain function. It is closely related, and in some cases subsumes, earlier unifying ideas such as Bayesian inference, predictive coding, and active learning. This article clarifies these connections, teasing apart distinctive and shared predictions.Comment: Accepted for publication in Neurons, Behavior, Data Analysis, and Theor

Representation learning with reward prediction errors

The Reward Prediction Error hypothesis proposes that phasic activity in the midbrain dopaminergic system reflects prediction errors needed for learning in reinforcement learning. Besides the well-documented association between dopamine and reward processing, dopamine is implicated in a variety of functions without a clear relationship to reward prediction error. Fluctuations in dopamine levels influence the subjective perception of time, dopamine bursts precede the generation of motor responses, and the dopaminergic system innervates regions of the brain, including hippocampus and areas in prefrontal cortex, whose function is not uniquely tied to reward. In this manuscript, we propose that a common theme linking these functions is representation, and that prediction errors signaled by the dopamine system, in addition to driving associative learning, can also support the acquisition of adaptive state representations. In a series of simulations, we show how this extension can account for the role of dopamine in temporal and spatial representation, motor response, and abstract categorization tasks. By extending the role of dopamine signals to learning state representations, we resolve a critical challenge to the Reward Prediction Error hypothesis of dopamine function

Evaluating Compositionality in Sentence Embeddings

An important challenge for human-like AI is compositional semantics. Recent research has attempted to address this by using deep neural networks to learn vector space embeddings of sentences, which then serve as input to other tasks. We present a new dataset for one such task, `natural language inference' (NLI), that cannot be solved using only word-level knowledge and requires some compositionality. We find that the performance of state of the art sentence embeddings (InferSent; Conneau et al., 2017) on our new dataset is poor. We analyze the decision rules learned by InferSent and find that they are consistent with simple heuristics that are ecologically valid in its training dataset. Further, we find that augmenting training with our dataset improves test performance on our dataset without loss of performance on the original training dataset. This highlights the importance of structured datasets in better understanding and improving AI systems

Building Machines That Learn and Think Like People

Recent progress in artificial intelligence (AI) has renewed interest in building systems that learn and think like people. Many advances have come from using deep neural networks trained end-to-end in tasks such as object recognition, video games, and board games, achieving performance that equals or even beats humans in some respects. Despite their biological inspiration and performance achievements, these systems differ from human intelligence in crucial ways. We review progress in cognitive science suggesting that truly human-like learning and thinking machines will have to reach beyond current engineering trends in both what they learn, and how they learn it. Specifically, we argue that these machines should (a) build causal models of the world that support explanation and understanding, rather than merely solving pattern recognition problems; (b) ground learning in intuitive theories of physics and psychology, to support and enrich the knowledge that is learned; and (c) harness compositionality and learning-to-learn to rapidly acquire and generalize knowledge to new tasks and situations. We suggest concrete challenges and promising routes towards these goals that can combine the strengths of recent neural network advances with more structured cognitive models.Comment: In press at Behavioral and Brain Sciences. Open call for commentary proposals (until Nov. 22, 2016). https://www.cambridge.org/core/journals/behavioral-and-brain-sciences/information/calls-for-commentary/open-calls-for-commentar

Where do hypotheses come from?

Why are human inferences sometimes remarkably close to the Bayesian ideal and other times systematically biased? One notable instance of this discrepancy is that tasks where the candidate hypotheses are explicitly available result in close to rational inference over the hypothesis space, whereas tasks requiring the self-generation of hypotheses produce systematic deviations from rational inference. We propose that these deviations arise from algorithmic processes approximating Bayes' rule. Specifically in our account, hypotheses are generated stochastically from a sampling process, such that the sampled hypotheses form a Monte Carlo approximation of the posterior. While this approximation will converge to the true posterior in the limit of infinite samples, we take a small number of samples as we expect that the number of samples humans take is limited by time pressure and cognitive resource constraints. We show that this model recreates several well-documented experimental findings such as anchoring and adjustment, subadditivity, superadditivity, the crowd within as well as the self-generation effect, the weak evidence, and the dud alternative effects. Additionally, we confirm the model's prediction that superadditivity and subadditivity can be induced within the same paradigm by manipulating the unpacking and typicality of hypotheses, in 2 experiments.This work was supported by the Center for Brains, Minds and Machines (CBMM), funded by NSF STC award CCF – 1231216

Perceptual multistability as Markov Chain Monte Carlo inference

While many perceptual and cognitive phenomena are well described in terms of Bayesian inference, the necessary computations are intractable at the scale of real-world tasks, and it remains unclear how the human mind approximates Bayesian computations algorithmically. We explore the proposal that for some tasks, humans use a form of Markov Chain Monte Carlo to approximate the posterior distribution over hidden variables. As a case study, we show how several phenomena of perceptual multistability can be explained as MCMC inference in simple graphical models for low-level vision

Successor-Predecessor Intrinsic Exploration

Exploration is essential in reinforcement learning, particularly in environments where external rewards are sparse. Here we focus on exploration with intrinsic rewards, where the agent transiently augments the external rewards with self-generated intrinsic rewards. Although the study of intrinsic rewards has a long history, existing methods focus on composing the intrinsic reward based on measures of future prospects of states, ignoring the information contained in the retrospective structure of transition sequences. Here we argue that the agent can utilise retrospective information to generate explorative behaviour with structure-awareness, facilitating efficient exploration based on global instead of local information. We propose Successor-Predecessor Intrinsic Exploration (SPIE), an exploration algorithm based on a novel intrinsic reward combining prospective and retrospective information. We show that SPIE yields more efficient and ethologically plausible exploratory behaviour in environments with sparse rewards and bottleneck states than competing methods. We also implement SPIE in deep reinforcement learning agents, and show that the resulting agent achieves stronger empirical performance than existing methods on sparse-reward Atari games

Distance Dependent Infinite Latent Feature Models

Latent feature models are widely used to decompose data into a small number of components. Bayesian nonparametric variants of these models, which use the Indian buffet process (IBP) as a prior over latent features, allow the number of features to be determined from the data. We present a generalization of the IBP, the distance dependent Indian buffet process (dd-IBP), for modeling non-exchangeable data. It relies on distances defined between data points, biasing nearby data to share more features. The choice of distance measure allows for many kinds of dependencies, including temporal and spatial. Further, the original IBP is a special case of the dd-IBP. In this paper, we develop the dd-IBP and theoretically characterize its feature-sharing properties. We derive a Markov chain Monte Carlo sampler for a linear Gaussian model with a dd-IBP prior and study its performance on several non-exchangeable data sets.Comment: 28 pages, 9 figure