ABSTRACT Neural networks have achieved state of the art performance across a wide variety of machine learning tasks, often with large and computation-heavy models. Inducing sparseness as a way to reduce the memory and computation footprint of these models has seen significant research attention in recent years. In this paper, we present a new method for dynamic sparseness, whereby part of the computations are omitted dynamically, based on the input. For e fficiency, we combined the idea of dynamic sparseness with block-wise matrix-vector multiplications. In contrast to static sparseness, which permanently zeroes out selected positions in weight matrices, our method preserves the full network capabilities by potentially accessing any trained weights. Y et, matrix vector multiplications are accelerated by omitting a predefined fraction of weight blocks from the matrix, based on the input. Experimental results on the task of language modeling, using recurrent and quasi-recurrent models, show that the proposed method can outperform a magnitude-based static sparseness baseline. In addition, our method achieves similar language modeling perplexities as the dense baseline, at half the computational cost at inference time. Introduction Deep Neural Networks (DNNs) have been a success story in recent years, due to their impressive performance on various domains. Theoretically and empirically, it has been shown that DNNs, trained by first-order-methods such as stochastic gradient decent (SGD), are able to represent a wide variety of complex functions (Hornik et al., 1989).

Variational Bayes is a method to find a good approximation of the posterior probability distribution of latent variables from a parametric family of distributions. The evidence lower bound (ELBO), which is nothing but the model evidence minus the Kullback-Leibler divergence, has been commonly used as a quality measure in the optimization process. However, the model evidence itself has been considered computationally intractable since it is expressed as a nested expectation with an outer expectation with respect to the training dataset and an inner conditional expectation with respect to latent variables. Similarly, if the Kullback-Leibler divergence is replaced with another divergence metric, the corresponding lower bound on the model evidence is often given by such a nested expectation. The standard (nested) Monte Carlo method can be used to estimate such quantities, whereas the resulting estimate is biased and the variance is often quite large. Recently the authors provided an unbiased estimator of the model evidence with small variance by applying the idea from multilevel Monte Carlo (MLMC) methods. In this article, we give more examples involving nested expectations in the context of variational Bayes where MLMC methods can help construct low-variance unbiased estimators, and provide numerical results which demonstrate the effectiveness of our proposed estimators.

A BSTRACT Most generative models of audio directly generate samples in one of two domains: time or frequency. While sufficient to express any signal, these representations are inefficient, as they do not utilize existing knowledge of how sound is generated and perceived. A third approach (vocoders/synthesizers) successfully incorporates strong domain knowledge of signal processing and perception, but has been less actively researched due to limited expressivity and difficulty integrating with modern auto-differentiation-based machine learning methods. In this paper, we introduce the Differentiable Digital Signal Processing (DDSP) library, which enables direct integration of classic signal processing elements with deep learning methods. Focusing on audio synthesis, we achieve high-fidelity generation without the need for large autoregressive models or adversarial losses, demonstrating that DDSP enables utilizing strong inductive biases without losing the expressive power of neural networks. Further, we show that combining interpretable modules permits manipulation of each separate model component, with applications such as independent control of pitch and loudness, realistic extrapolation to pitches not seen during training, blind dereverberation of room acoustics, transfer of extracted room acoustics to new environments, and transformation of timbre between disparate sources. In short, DDSP enables an interpretable and modular approach to generative modeling, without sacrificing the benefits of deep learning. The library is publicly available 1 and we welcome further contributions from the community and domain experts. 1 I NTRODUCTION Neural networks are universal function approximators in the asymptotic limit (Hornik et al., 1989), but their practical success is largely due to the use of strong structural priors such as convolution (Le-Cun et al., 1989), recurrence (Sutskever et al., 2014; Williams & Zipser, 1990; Werbos, 1990), and self-attention (V aswani et al., 2017). These architectural constraints promote generalization and data efficiency to the extent that they align with the data domain. From this perspective, end-to-end learning relies on structural priors to scale, but the practitioner's toolbox is limited to functions that can be expressed differentiably. Here, we increase the size of that toolbox by introducing the Differentiable Digital Signal Processing (DDSP) library, which integrates interpretable signal processing elements into modern automatic differentiation software (TensorFlow). While this approach has broad applicability, we highlight its potential in this paper through exploring the example of audio synthesis.

This paper presents a new approach to a robust Gaussian process (GP) regression. Most existing approaches replace an outlier-prone Gaussian likelihood with a non-Gaussian likelihood induced from a heavy tail distribution, such as the Laplace distribution and Student-t distribution. However, the use of a non-Gaussian likelihood would incur the need for a computationally expensive Bayesian approximate computation in the posterior inferences. The proposed approach models an outlier as a noisy and biased observation of an unknown regression function, and accordingly, the likelihood contains bias terms to explain the degree of deviations from the regression function. We entail how the biases can be estimated accurately with other hyperparameters by a regularized maximum likelihood estimation. Conditioned on the bias estimates, the robust GP regression can be reduced to a standard GP regression problem with analytical forms of the predictive mean and variance estimates. Therefore, the proposed approach is simple and very computationally attractive. It also gives a very robust and accurate GP estimate for many tested scenarios. For the numerical evaluation, we perform a comprehensive simulation study to evaluate the proposed approach with the comparison to the existing robust GP approaches under various simulated scenarios of different outlier proportions and different noise levels. The approach is applied to data from two measurement systems, where the predictors are based on robust environmental parameter measurements and the response variables utilize more complex chemical sensing methods that contain a certain percentage of outliers. The utility of the measurement systems and value of the environmental data are improved through the computationally efficient GP regression and bias model.

An optimal dynamic treatment regime (DTR) consists of a sequence of decision rules in maximizing long-term benefits, which is applicable for chronic diseases such as HIV infection or cancer. In this paper, we develop a novel angle-based approach to search the optimal DTR under a multicategory treatment framework for survival data. The proposed method targets maximization the conditional survival function of patients following a DTR. In contrast to most existing approaches which are designed to maximize the expected survival time under a binary treatment framework, the proposed method solves the multicategory treatment problem given multiple stages for censored data. Specifically, the proposed method obtains the optimal DTR via integrating estimations of decision rules at multiple stages into a single multicategory classification algorithm without imposing additional constraints, which is also more computationally efficient and robust. In theory, we establish Fisher consistency of the proposed method under regularity conditions. Our numerical studies show that the proposed method outperforms competing methods in terms of maximizing the conditional survival function. We apply the proposed method to two real datasets: Framingham heart study data and acquired immunodeficiency syndrome (AIDS) clinical data.

Abstract--In this paper, we examine the fundamental performance limitations of online machine learning, by viewing th e online learning problem as a prediction problem with causal side information. T owards this end, we combine the entropic analysis from information theory and the innovations appro ach from prediction theory to derive generic lower bounds on the prediction errors as well as the conditions (in terms of, e.g., d irected information) to achieve the bounds. It is seen in general tha t no specific restrictions have to be imposed on the learning algo rithms or the distributions of the data points for the performance b ounds to be valid. In addition, the cases of supervised learning, s emi-supervised learning, as well as unsupervised learning can a ll be analyzed accordingly. We also investigate the implication s of the results in analyzing the fundamental limits of generalizat ion.

Despite the growing interest in continual learning, most of its contemporary works have been studied in a rather restricted setting where tasks are clearly distinguishable, and task boundaries are known during training. However, if our goal is to develop an algorithm that learns as humans do, this setting is far from realistic, and it is essential to develop a methodology that works in a task-free manner. Meanwhile, among several branches of continual learning, expansion-based methods have the advantage of eliminating catastrophic forgetting by allocating new resources to learn new data. In this work, we propose an expansion-based approach for task-free continual learning. Our model, named Continual Neural Dirichlet Process Mixture (CN-DPM), consists of a set of neural network experts that are in charge of a subset of the data. CN-DPM expands the number of experts in a principled way under the Bayesian nonparametric framework. With extensive experiments, we show that our model successfully performs task-free continual learning for both discriminative and generative tasks such as image classification and image generation.

Traveling salesman problem ( TSP) is a well-known in computing field. There are many researches to improve the genetic algorithm for solving TSP. In this paper, we propose two new crossover operators and new mechanism of combination crossover operators in genetic algorithm for solving TSP. We experimented on TSP instances from TSP -Lib and compared the results of proposed algorithm with genetic algorithm ( GA), which used MSCX. Experimental results show that, our proposed algorithm is better than the GA using MSCX on the min, mean cost values.

To support human decision making with machine learning models, we often need to elucidate patterns embedded in the models that are unsalient, unknown, or counterintuitive to humans. While existing approaches focus on explaining machine predictions with real-time assistance, we explore model-driven tutorials to help humans understand these patterns in a training phase. We consider both tutorials with guidelines from scientific papers, analogous to current practices of science communication, and automatically selected examples from training data with explanations. We use deceptive review detection as a testbed and conduct large-scale, randomized human-subject experiments to examine the effectiveness of such tutorials. We find that tutorials indeed improve human performance, with and without real-time assistance. In particular, although deep learning provides superior predictive performance than simple models, tutorials and explanations from simple models are more useful to humans. Our work suggests future directions for human-centered tutorials and explanations towards a synergy between humans and AI.

High-dimensional data and high-dimensional representations of reality are inherent features of modern Artificial Intelligence systems and applications of machine learning. The well-known phenomenon of the "curse of dimensionality" states: many problems become exponentially difficult in high dimensions. Recently, the other side of the coin, the "blessing of dimensionality", has attracted much attention. It turns out that generic high-dimensional datasets exhibit fairly simple geometric properties. Thus, there is a fundamental tradeoff between complexity and simplicity in high dimensional spaces. Here we present a brief explanatory review of recent ideas, results and hypotheses about the blessing of dimensionality and related simplifying effects relevant to machine learning and neuroscience.