1,080 research outputs found
Non-negative matrix factorization with sparseness constraints
Non-negative matrix factorization (NMF) is a recently developed technique for
finding parts-based, linear representations of non-negative data. Although it
has successfully been applied in several applications, it does not always
result in parts-based representations. In this paper, we show how explicitly
incorporating the notion of `sparseness' improves the found decompositions.
Additionally, we provide complete MATLAB code both for standard NMF and for our
extension. Our hope is that this will further the application of these methods
to solving novel data-analysis problems
Better Optimism By Bayes: Adaptive Planning with Rich Models
The computational costs of inference and planning have confined Bayesian
model-based reinforcement learning to one of two dismal fates: powerful
Bayes-adaptive planning but only for simplistic models, or powerful, Bayesian
non-parametric models but using simple, myopic planning strategies such as
Thompson sampling. We ask whether it is feasible and truly beneficial to
combine rich probabilistic models with a closer approximation to fully Bayesian
planning. First, we use a collection of counterexamples to show formal problems
with the over-optimism inherent in Thompson sampling. Then we leverage
state-of-the-art techniques in efficient Bayes-adaptive planning and
non-parametric Bayesian methods to perform qualitatively better than both
existing conventional algorithms and Thompson sampling on two contextual
bandit-like problems.Comment: 11 pages, 11 figure
Efficient Bayes-Adaptive Reinforcement Learning using Sample-Based Search
Bayesian model-based reinforcement learning is a formally elegant approach to
learning optimal behaviour under model uncertainty, trading off exploration and
exploitation in an ideal way. Unfortunately, finding the resulting
Bayes-optimal policies is notoriously taxing, since the search space becomes
enormous. In this paper we introduce a tractable, sample-based method for
approximate Bayes-optimal planning which exploits Monte-Carlo tree search. Our
approach outperformed prior Bayesian model-based RL algorithms by a significant
margin on several well-known benchmark problems -- because it avoids expensive
applications of Bayes rule within the search tree by lazily sampling models
from the current beliefs. We illustrate the advantages of our approach by
showing it working in an infinite state space domain which is qualitatively out
of reach of almost all previous work in Bayesian exploration.Comment: 14 pages, 7 figures, includes supplementary material. Advances in
Neural Information Processing Systems (NIPS) 201
Probabilistic Meta-Representations Of Neural Networks
Existing Bayesian treatments of neural networks are typically characterized
by weak prior and approximate posterior distributions according to which all
the weights are drawn independently. Here, we consider a richer prior
distribution in which units in the network are represented by latent variables,
and the weights between units are drawn conditionally on the values of the
collection of those variables. This allows rich correlations between related
weights, and can be seen as realizing a function prior with a Bayesian
complexity regularizer ensuring simple solutions. We illustrate the resulting
meta-representations and representations, elucidating the power of this prior.Comment: presented at UAI 2018 Uncertainty In Deep Learning Workshop (UDL AUG.
2018
Monte Carlo Planning method estimates planning horizons during interactive social exchange
Reciprocating interactions represent a central feature of all human
exchanges. They have been the target of various recent experiments, with
healthy participants and psychiatric populations engaging as dyads in
multi-round exchanges such as a repeated trust task. Behaviour in such
exchanges involves complexities related to each agent's preference for equity
with their partner, beliefs about the partner's appetite for equity, beliefs
about the partner's model of their partner, and so on. Agents may also plan
different numbers of steps into the future. Providing a computationally precise
account of the behaviour is an essential step towards understanding what
underlies choices. A natural framework for this is that of an interactive
partially observable Markov decision process (IPOMDP). However, the various
complexities make IPOMDPs inordinately computationally challenging. Here, we
show how to approximate the solution for the multi-round trust task using a
variant of the Monte-Carlo tree search algorithm. We demonstrate that the
algorithm is efficient and effective, and therefore can be used to invert
observations of behavioural choices. We use generated behaviour to elucidate
the richness and sophistication of interactive inference
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