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Register a new userOn Universal Features for High-Dimensional Learning and Inference
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Added by
Gregory Wornell
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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We consider the problem of identifying universal low-dimensional features from high-dimensional data for inference tasks in settings involving learning. For such problems, we introduce natural notions of universality and we show a local equivalence among them. Our analysis is naturally expressed via information geometry, and represents a conceptually and computationally useful analysis. The development reveals the complementary roles of the singular value decomposition, Hirschfeld-Gebelein-Renyi maximal correlation, the canonical correlation and principle component analyses of Hotelling and Pearson, Tishbys information bottleneck, Wyners common information, Ky Fan $k$-norms, and Brieman and Friedmans alternating conditional expectations algorithm. We further illustrate how this framework facilitates understanding and optimizing aspects of learning systems, including multinomial logistic (softmax) regression and the associated neural network architecture, matrix factorization methods for collaborative filtering and other applications, rank-constrained multivariate linear regression, and forms of semi-supervised learning.
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This paper presents a new approach, called perturb-max, for high-dimensional statistical inference that is based on applying random perturbations followed by optimization. This framework injects randomness to maximum a-posteriori (MAP) predictors by randomly perturbing the potential function for the input. A classic result from extreme value statistics asserts that perturb-max operations generate unbiased samples from the Gibbs distribution using high-dimensional perturbations. Unfortunately, the computational cost of generating so many high-dimensional random variables can be prohibitive. However, when the perturbations are of low dimension, sampling the perturb-max prediction is as efficient as MAP optimization. This paper shows that the expected value of perturb-max inference with low dimensional perturbations can be used sequentially to generate unbiased samples from the Gibbs distribution. Furthermore the expected value of the maximal perturbations is a natural bound on the entropy of such perturb-max models. A measure concentration result for perturb-max values shows that the deviation of their sampled average from its expectation decays exponentially in the number of samples, allowing effective approximation of the expectation.
Transfer in Reinforcement Learning (RL) refers to the idea of applying knowledge gained from previous tasks to solving related tasks. Learning a universal value function (Schaul et al., 2015), which generalizes over goals and states, has previously been shown to be useful for transfer. However, successor features are believed to be more suitable than values for transfer (Dayan, 1993; Barreto et al.,2017), even though they cannot directly generalize to new goals. In this paper, we propose (1) Universal Successor Features (USFs) to capture the underlying dynamics of the environment while allowing generalization to unseen goals and (2) a flexible end-to-end model of USFs that can be trained by interacting with the environment. We show that learning USFs is compatible with any RL algorithm that learns state values using a temporal difference method. Our experiments in a simple gridworld and with two MuJoCo environments show that USFs can greatly accelerate training when learning multiple tasks and can effectively transfer knowledge to new tasks.
Todays intelligent applications can achieve high performance accuracy using machine learning (ML) techniques, such as deep neural networks (DNNs). Traditionally, in a remote DNN inference problem, an edge device transmits raw data to a remote node that performs the inference task. However, this may incur high transmission energy costs and puts data privacy at risk. In this paper, we propose a technique to reduce the total energy bill at the edge device by utilizing model compression and time-varying model split between the edge and remote nodes. The time-varying representation accounts for time-varying channels and can significantly reduce the total energy at the edge device while maintaining high accuracy (low loss). We implement our approach in an image classification task using the MNIST dataset, and the system environment is simulated as a trajectory navigation scenario to emulate different channel conditions. Numerical simulations show that our proposed solution results in minimal energy consumption and $CO_2$ emission compared to the considered baselines while exhibiting robust performance across different channel conditions and bandwidth regime choices.
The design of methods for inference from time sequences has traditionally relied on statistical models that describe the relation between a latent desired sequence and the observed one. A broad family of model-based algorithms have been derived to carry out inference at controllable complexity using recursive computations over the factor graph representing the underlying distribution. An alternative model-agnostic approach utilizes machine learning (ML) methods. Here we propose a framework that combines model-based algorithms and data-driven ML tools for stationary time sequences. In the proposed approach, neural networks are developed to separately learn specific components of a factor graph describing the distribution of the time sequence, rather than the complete inference task. By exploiting stationary properties of this distribution, the resulting approach can be applied to sequences of varying temporal duration. Learned factor graph can be realized using compact neural networks that are trainable using small training sets, or alternatively, be used to improve upon existing deep inference systems. We present an inference algorithm based on learned stationary factor graphs, which learns to implement the sum-product scheme from labeled data, and can be applied to sequences of different lengths. Our experimental results demonstrate the ability of the proposed learned factor graphs to learn to carry out accurate inference from small training sets for sleep stage detection using the Sleep-EDF dataset, as well as for symbol detection in digital communications with unknown channels.
Splitting network computations between the edge device and a server enables low edge-compute inference of neural networks but might expose sensitive information about the test query to the server. To address this problem, existing techniques train the model to minimize information leakage for a given set of sensitive attributes. In practice, however, the test queries might contain attributes that are not foreseen during training. We propose instead an unsupervised obfuscation method to discard the information irrelevant to the main task. We formulate the problem via an information theoretical framework and derive an analytical solution for a given distortion to the model output. In our method, the edge device runs the model up to a split layer determined based on its computational capacity. It then obfuscates the obtained feature vector based on the first layer of the server model by removing the components in the null space as well as the low-energy components of the remaining signal. Our experimental results show that our method outperforms existing techniques in removing the information of the irrelevant attributes and maintaining the accuracy on the target label. We also show that our method reduces the communication cost and incurs only a small computational overhead.
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