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Publications
Tensor Networks for Probabilistic Sequence Modeling
Tensor networks are a powerful modeling framework developed for computational many-body physics, which have only recently been applied withi… (see more)n machine learning. In this work we utilize a uniform matrix product state (u-MPS) model for probabilistic modeling of sequence data. We first show that u-MPS enable sequence-level parallelism, with length-n sequences able to be evaluated in depth O(log n). We then introduce a novel generative algorithm giving trained u-MPS the ability to efficiently sample from a wide variety of conditional distributions, each one defined by a regular expression. Special cases of this algorithm correspond to autoregressive and fill-in-the-blank sampling, but more complex regular expressions permit the generation of richly structured text in a manner that has no direct analogue in current generative models. Experiments on synthetic text data find u-MPS outperforming LSTM baselines in several sampling tasks, and demonstrate strong generalization in the presence of limited data.
2020-03-02
International Conference on Artificial Intelligence and Statistics (published)
Tensor networks are a powerful modeling framework developed for computational many-body physics, which have only recently been applied withi… (see more)n machine learning. In this work we utilize a uniform matrix product state (u-MPS) model for probabilistic modeling of sequence data. We first show that u-MPS enable sequence-level parallelism, with length-n sequences able to be evaluated in depth O(log n). We then introduce a novel generative algorithm giving trained u-MPS the ability to efficiently sample from a wide variety of conditional distributions, each one defined by a regular expression. Special cases of this algorithm correspond to autoregressive and fill-in-the-blank sampling, but more complex regular expressions permit the generation of richly structured text in a manner that has no direct analogue in current generative models. Experiments on synthetic text data find u-MPS outperforming LSTM baselines in several sampling tasks, and demonstrate strong generalization in the presence of limited data.
2020-03-02
International Conference on Artificial Intelligence and Statistics (published)
Model-free deep reinforcement learning is sample inefficient. One hypothesis -- speculated, but not confirmed -- is that catastrophic interf… (see more)erence within an environment inhibits learning. We test this hypothesis through a large-scale empirical study in the Arcade Learning Environment (ALE) and, indeed, find supporting evidence. We show that interference causes performance to plateau; the network cannot train on segments beyond the plateau without degrading the policy used to reach there. By synthetically controlling for interference, we demonstrate performance boosts across architectures, learning algorithms and environments. A more refined analysis shows that learning one segment of a game often increases prediction errors elsewhere. Our study provides a clear empirical link between catastrophic interference and sample efficiency in reinforcement learning.
Normalizing flows are powerful invertible probabilistic models that can be used to translate two probability distributions, in a way that al… (see more)lows us to efficiently track the change of probability density. However, to trade for computational efficiency in sampling and in evaluating the log-density, special parameterization designs have been proposed at the cost of representational expressiveness. In this work, we propose to use ODEs as a framework to establish universal approximation theory for certain families of flow-based models.
2020-02-26
International Conference on Learning Representations (published)
Network connectivity fingerprints are among today's best choices to obtain a faithful sampling of an individual's brain and cognition. Widel… (see more)y available MRI scanners can provide rich information tapping into network recruitment and reconfiguration that now scales to hundreds and thousands of humans. Here, we contemplate the advantages of analysing such connectome profiles using Bayesian strategies. These analysis techniques afford full probability estimates of the studied network coupling phenomena, provide analytical machinery to separate epistemological uncertainty and biological variability in a coherent manner, usher us towards avenues to go beyond binary statements on existence versus non-existence of an effect, and afford credibility estimates around all model parameters at play which thus enable single-subject predictions with rigorous uncertainty intervals. We illustrate the brittle boundary between healthy and diseased brain circuits by autism spectrum disorder as a recurring theme where, we argue, network-based approaches in neuroscience will require careful probabilistic answers. This article is part of the theme issue ‘Unifying the essential concepts of biological networks: biological insights and philosophical foundations’.
2020-02-24
Philosophical Transactions of the Royal Society of London. Biological Sciences (published)
We propose a stochastic variant of the classical Polyak step-size (Polyak, 1987) commonly used in the subgradient method. Although computing… (see more) the Polyak step-size requires knowledge of the optimal function values, this information is readily available for typical modern machine learning applications. Consequently, the proposed stochastic Polyak step-size (SPS) is an attractive choice for setting the learning rate for stochastic gradient descent (SGD). We provide theoretical convergence guarantees for SGD equipped with SPS in different settings, including strongly convex, convex and non-convex functions. Furthermore, our analysis results in novel convergence guarantees for SGD with a constant step-size. We show that SPS is particularly effective when training over-parameterized models capable of interpolating the training data. In this setting, we prove that SPS enables SGD to converge to the true solution at a fast rate without requiring the knowledge of any problem-dependent constants or additional computational overhead. We experimentally validate our theoretical results via extensive experiments on synthetic and real datasets. We demonstrate the strong performance of SGD with SPS compared to state-of-the-art optimization methods when training over-parameterized models.
In this work, we propose a new family of generative flows on an augmented data space, with an aim to improve expressivity without drasticall… (see more)y increasing the computational cost of sampling and evaluation of a lower bound on the likelihood. Theoretically, we prove the proposed flow can approximate a Hamiltonian ODE as a universal transport map. Empirically, we demonstrate state-of-the-art performance on standard benchmarks of flow-based generative modeling.
