Resource-Efficient Neural Networks for Embedded Systems

While machine learning is traditionally a resource intensive task, embedded systems, autonomous navigation, and the vision of the Internet of Things fuel the interest in resource-efficient approaches. These approaches aim for a carefully chosen trade-off between performance and resource consumption in terms of computation and energy. The development of such approaches is among the major challenges in current machine learning research and key to ensure a smooth transition of machine learning technology from a scientific environment with virtually unlimited computing resources into every day's applications. In this article, we provide an overview of the current state of the art of machine learning techniques facilitating these real-world requirements. In particular, we focus on deep neural networks (DNNs), the predominant machine learning models of the past decade. We give a comprehensive overview of the vast literature that can be mainly split into three non-mutually exclusive categories: (i) quantized neural networks, (ii) network pruning, and (iii) structural efficiency. These techniques can be applied during training or as post-processing, and they are widely used to reduce the computational demands in terms of memory footprint, inference speed, and energy efficiency. We substantiate our discussion with experiments on well-known benchmark data sets to showcase the difficulty of finding good trade-offs between resource-efficiency and predictive performance.

Bayesian Learning of Sum-Product Networks

Sum-product networks (SPNs) are flexible density estimators and have received significant attention, due to their attractive inference properties. While parameter learning in SPNs is well developed, structure learning leaves something to be desired: Even though there is a plethora of SPN structure learners, most of them are somewhat ad-hoc, and based on intuition rather than a clear learning principle. In this paper, we introduce a well-principled Bayesian framework for SPN structure learning. First, we decompose the problem into i) laying out a basic computational graph, and ii) learning the so-called scope function over the graph. The first is rather unproblematic and akin to neural network architecture validation. The second characterises the effective structure of the SPN and needs to respect the usual structural constraints in SPN, i.e. completeness and decomposability. While representing and learning the scope function is rather involved in general, in this paper, we propose a natural parametrisation for an important and widely used special case of SPNs. These structural parameters are incorporated into a Bayesian model, such that simultaneous structure and parameter learning is cast into monolithic Bayesian posterior inference. In various experiments, our Bayesian SPNs often improve test likelihoods over greedy SPN learners. Further, since the Bayesian framework protects against overfitting, we are able to evaluate hyper-parameters directly on the Bayesian model score, waiving the need for a separate validation set, which is especially beneficial in low data regimes. Bayesian SPNs can be applied to heterogeneous domains and can easily be extended to nonparametric formulations. Moreover, our Bayesian approach is the first which consistently and robustly learns SPN structures under missing data.

Efficient and Robust Machine Learning for Real-World Systems

While machine learning is traditionally a resource intensive task, embedded systems, autonomous navigation and the vision of the Internet-of-Things fuel the interest in resource efficient approaches. These approaches require a carefully chosen trade-off between performance and resource consumption in terms of computation and energy. On top of this, it is crucial to treat uncertainty in a consistent manner in all but the simplest applications of machine learning systems. In particular, a desideratum for any real-world system is to be robust in the presence of outliers and corrupted data, as well as being `aware' of its limits, i.e.\ the system should maintain and provide an uncertainty estimate over its own predictions. These complex demands are among the major challenges in current machine learning research and key to ensure a smooth transition of machine learning technology into every day's applications. In this article, we provide an overview of the current state of the art of machine learning techniques facilitating these real-world requirements. First we provide a comprehensive review of resource-efficiency in deep neural networks with focus on techniques for model size reduction, compression and reduced precision. These techniques can be applied during training or as post-processing and are widely used to reduce both computational complexity and memory footprint. As most (practical) neural networks are limited in their ways to treat uncertainty, we contrast them with probabilistic graphical models, which readily serve these desiderata by means of probabilistic inference. In that way, we provide an extensive overview of the current state-of-the-art of robust and efficient machine learning for real-world systems.

Handling Incomplete Heterogeneous Data using VAEs

Variational autoencoders (VAEs), as well as other generative models, have been shown to be efficient and accurate to capture the latent structure of vast amounts of complex high-dimensional data. However, existing VAEs can still not directly handle data that are heterogenous (mixed continuous and discrete) or incomplete (with missing data at random), which is indeed common in real-world applications. In this paper, we propose a general framework to design VAEs, suitable for fitting incomplete heterogenous data. The proposed HI-VAE includes likelihood models for real-valued, positive real valued, interval, categorical, ordinal and count data, and allows to estimate (and potentially impute) missing data accurately. Furthermore, HI-VAE presents competitive predictive performance in supervised tasks, outperforming super- vised models when trained on incomplete data

Automatic Bayesian Density Analysis

Making sense of a dataset in an automatic and unsupervised fashion is a challenging problem in statistics and AI. Classical approaches for density estimation are usually not flexible enough to deal with the uncertainty inherent to real-world data: they are often restricted to fixed latent interaction models and homogeneous likelihoods; they are sensitive to missing, corrupt and anomalous data; moreover, their expressiveness generally comes at the price of intractable inference. As a result, supervision from statisticians is usually needed to find the right model for the data. However, as domain experts do not necessarily have to be experts in statistics, we propose Automatic Bayesian Density Analysis (ABDA) to make density estimation accessible at large. ABDA automates the selection of adequate likelihood models from arbitrarily rich dictionaries while modeling their interactions via a deep latent structure adaptively learned from data as a sum-product network. ABDA casts uncertainty estimation at these local and global levels into a joint Bayesian inference problem, providing robust and yet tractable inference. Extensive empirical evidence shows that ABDA is a suitable tool for automatic exploratory analysis of heterogeneous tabular data, allowing for missing value estimation, statistical data type and likelihood discovery, anomaly detection and dependency structure mining, on top of providing accurate density estimation.

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.

Gaussian Process Behaviour in Wide Deep Neural Networks

Whilst deep neural networks have shown great empirical success, there is still much work to be done to understand their theoretical properties. In this paper, we study the relationship between random, wide, fully connected, feedforward networks with more than one hidden layer and Gaussian processes with a recursive kernel definition. We show that, under broad conditions, as we make the architecture increasingly wide, the implied random function converges in distribution to a Gaussian process, formalising and extending existing results by Neal (1996) to deep networks. To evaluate convergence rates empirically, we use maximum mean discrepancy. We then compare finite Bayesian deep networks from the literature to Gaussian processes in terms of the key predictive quantities of interest, finding that in some cases the agreement can be very close. We discuss the desirability of Gaussian process behaviour and review non-Gaussian alternative models from the literature.

Ergodic Measure Preserving Flows

Probabilistic modelling is a general and elegant framework to capture the uncertainty, ambiguity and diversity of data. Probabilistic inference is the core technique for developing training and simulation algorithms on probabilistic models. However, the classic inference methods, like Markov chain Monte Carlo (MCMC) methods and mean-field variational inference (VI), are not computationally scalable for the recent developed probabilistic models with neural networks (NNs). This motivates many recent works on improving classic inference methods using NNs, especially, NN empowered VI. However, even with powerful NNs, VI still suffers its fundamental limitations. In this work, we propose a novel computational scalable general inference framework. With the theoretical foundation in ergodic theory, the proposed methods are not only computationally scalable like NN-based VI methods but also asymptotically accurate like MCMC. We test our method on popular benchmark problems and the results suggest that our methods can outperform NN-based VI and MCMC on deep generative models and Bayesian neural networks.

Antithetic and Monte Carlo kernel estimators for partial rankings

In the modern age, rankings data is ubiquitous and it is useful for a variety of applications such as recommender systems, multi-object tracking and preference learning. However, most rankings data encountered in the real world is incomplete, which prevents the direct application of existing modelling tools for complete rankings. Our contribution is a novel way to extend kernel methods for complete rankings to partial rankings, via consistent Monte Carlo estimators for Gram matrices: matrices of kernel values between pairs of observations. We also present a novel variance reduction scheme based on an antithetic variate construction between permutations to obtain an improved estimator for the Mallows kernel. The corresponding antithetic kernel estimator has lower variance and we demonstrate empirically that it has a better performance in a variety of Machine Learning tasks. Both kernel estimators are based on extending kernel mean embeddings to the embedding of a set of full rankings consistent with an observed partial ranking. They form a computationally tractable alternative to previous approaches for partial rankings data. An overview of the existing kernels and metrics for permutations is also provided.

Few-shot learning of neural networks from scratch by pseudo example optimization

In this paper, we propose a simple but effective method for training neural networks with a limited amount of training data. Our approach inherits the idea of knowledge distillation that transfers knowledge from a deep or wide reference model to a shallow or narrow target model. The proposed method employs this idea to mimic predictions of reference estimators that are more robust against overfitting than the network we want to train. Different from almost all the previous work for knowledge distillation that requires a large amount of labeled training data, the proposed method requires only a small amount of training data. Instead, we introduce pseudo training examples that are optimized as a part of model parameters. Experimental results for several benchmark datasets demonstrate that the proposed method outperformed all the other baselines, such as naive training of the target model and standard knowledge distillation.