Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userExchangeable Variable Models
437
0
0.0
(
0
)
Added by
Mathias Niepert
Publication date
2014
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
A sequence of random variables is exchangeable if its joint distribution is invariant under variable permutations. We introduce exchangeable variable models (EVMs) as a novel class of probabilistic models whose basic building blocks are partially exchangeable sequences, a generalization of exchangeable sequences. We prove that a family of tractable EVMs is optimal under zero-one loss for a large class of functions, including parity and threshold functions, and strictly subsumes existing tractable independence-based model families. Extensive experiments show that EVMs outperform state of the art classifiers such as SVMs and probabilistic models which are solely based on independence assumptions.
rate research
Read More
Poor sample efficiency is a major limitation of deep reinforcement learning in many domains. This work presents an attention-based method to project neural network inputs into an efficient representation space that is invariant under changes to input ordering. We show that our proposed representation results in an input space that is a factor of $m!$ smaller for inputs of $m$ objects. We also show that our method is able to represent inputs over variable numbers of objects. Our experiments demonstrate improvements in sample efficiency for policy gradient methods on a variety of tasks. We show that our representation allows us to solve problems that are otherwise intractable when using naive approaches.
We investigate permutation-invariant continuous variable quantum states and their covariance matrices. We provide a complete characterization of the latter with respect to permutation-invariance, exchangeability and representing convex combinations of tensor power states. On the level of the respective density operators this leads to necessary criteria for all these properties which become necessary and sufficient for Gaussian states. For these we use the derived results to provide de Finetti-type theorems for various distance measures.
The recurrent neural networks (RNN) with richly distributed internal states and flexible non-linear transition functions, have overtaken the dynamic Bayesian networks such as the hidden Markov models (HMMs) in the task of modeling highly structured sequential data. These data, such as from speech and handwriting, often contain complex relationships between the underlaying variational factors and the observed data. The standard RNN model has very limited randomness or variability in its structure, coming from the output conditional probability model. This paper will present different ways of using high level latent random variables in RNN to model the variability in the sequential data, and the training method of such RNN model under the VAE (Variational Autoencoder) principle. We will explore possible ways of using adversarial method to train a variational RNN model. Contrary to competing approaches, our approach has theoretical optimum in the model training and provides better model training stability. Our approach also improves the posterior approximation in the variational inference network by a separated adversarial training step. Numerical results simulated from TIMIT speech data show that reconstruction loss and evidence lower bound converge to the same level and adversarial training loss converges to 0.
Recently there has been growing interest in modeling sets with exchangeability such as point clouds. A shortcoming of current approaches is that they restrict the cardinality of the sets considered or can only express limited forms of distribution over unobserved data. To overcome these limitations, we introduce Energy-Based Processes (EBPs), which extend energy based models to exchangeable data while allowing neural network parameterizations of the energy function. A key advantage of these models is the ability to express more flexible distributions over sets without restricting their cardinality. We develop an efficient training procedure for EBPs that demonstrates state-of-the-art performance on a variety of tasks such as point cloud generation, classification, denoising, and image completion.
In this paper, we focus on the problem of stable prediction across unknown test data, where the test distribution is agnostic and might be totally different from the training one. In such a case, previous machine learning methods might exploit subtly spurious correlations in training data induced by non-causal variables for prediction. Those spurious correlations are changeable across data, leading to instability of prediction across data. By assuming the relationships between causal variables and response variable are invariant across data, to address this problem, we propose a conditional independence test based algorithm to separate those causal variables with a seed variable as priori, and adopt them for stable prediction. By assuming the independence between causal and non-causal variables, we show, both theoretically and with empirical experiments, that our algorithm can precisely separate causal and non-causal variables for stable prediction across test data. Extensive experiments on both synthetic and real-world datasets demonstrate that our algorithm outperforms state-of-the-art methods for stable prediction.
suggested questions
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
