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This paper proposes a novel Gaussian process approach to fault removal in time-series data. Fault removal does not delete the faulty signal data but, instead, massages the fault from the data. We assume that only one fault occurs at any one time and model the signal by two separate non-parametric Gaussian process models for both the physical phenomenon and the fault. In order to facilitate fault removal we introduce the Markov Region Link kernel for handling non-stationary Gaussian processes. This kernel is piece-wise stationary but guarantees that functions generated by it and their derivatives (when required) are everywhere continuous. We apply this kernel to the removal of drift and bias errors in faulty sensor data and also to the recovery of EOG artifact corrupted EEG signals., Comment: 9 pages, 14 figures

We introduce a novel Bayesian approach to global optimization using Gaussian processes. We frame the optimization of both noisy and noiseless functions as sequential decision problems, and introduce myopic and non-myopic solutions to them. Here our solutions can be tailored to exactly the degree of confidence we require of them. The use of Gaussian processes allows us to benefit from the incorporation of prior knowledge about our objective function, and also from any derivative observations. Using this latter fact, we introduce an innovative method to combat conditioning problems. Our algorithm demonstrates a significant improvement over its competitors in overall performance across a wide range of canonical test problems.

Leveraging the wealth of unlabeled data produced in recent years provides great potential for improving supervised models. When the cost of acquiring labels is high, probabilistic active learning methods can be used to greedily select the most informative data points to be labeled. However, for many large-scale problems standard greedy procedures become computationally infeasible and suffer from negligible model change. In this paper, we introduce a novel Bayesian batch active learning approach that mitigates these issues. Our approach is motivated by approximating the complete data posterior of the model parameters. While naive batch construction methods result in correlated queries, our algorithm produces diverse batches that enable efficient active learning at scale. We derive interpretable closed-form solutions akin to existing active learning procedures for linear models, and generalize to arbitrary models using random projections. We demonstrate the benefits of our approach on several large-scale regression and classification tasks.

Lossless compression methods shorten the expected representation size of data without loss of information, using a statistical model. Flow-based models are attractive in this setting because they admit exact likelihood optimization, which is equivalent to minimizing the expected number of bits per message. However, conventional flows assume continuous data, which may lead to reconstruction errors when quantized for compression. For that reason, we introduce a flow-based generative model for ordinal discrete data called Integer Discrete Flow (IDF): a bijective integer map that can learn rich transformations on high-dimensional data. As building blocks for IDFs, we introduce a flexible transformation layer called integer discrete coupling. Our experiments show that IDFs are competitive with other flow-based generative models. Furthermore, we demonstrate that IDF based compression achieves state-of-the-art lossless compression rates on CIFAR10, ImageNet32, and ImageNet64. To the best of our knowledge, this is the first lossless compression method that uses invertible neural networks.

This paper focuses on Bayesian Optimization (BO) for objectives on combinatorial search spaces, including ordinal and categorical variables. Despite the abundance of potential applications of Combinatorial BO, including chipset configuration search and neural architecture search, only a handful of methods have been proposed. We introduce COMBO, a new Gaussian Process (GP) BO. COMBO quantifies “smoothness” of functions on combinatorial search spaces by utilizing a combinatorial graph. The vertex set of the combinatorial graph consists of all possible joint assignments of the variables, while edges are constructed using the graph Cartesian product of the sub-graphs that represent the individual variables. On this combinatorial graph, we propose an ARD diffusion kernel with which the GP is able to model high-order interactions between variables leading to better performance. Moreover, using the Horseshoe prior for the scale parameter in the ARD diffusion kernel results in an effective variable selection procedure, making COMBO suitable for high dimensional problems. Computationally, in COMBO the graph Cartesian product allows the Graph Fourier Transform calculation to scale linearly instead of exponentially. We validate COMBO in a wide array of realistic benchmarks, including weighted maximum satisfiability problems and neural architecture search. COMBO outperforms consistently the latest state-of-the-art while maintaining computational and statistical efficiency

This paper introduces hyperspherical prototype networks, which unify classification and regression with prototypes on hyperspherical output spaces. For classification, a common approach is to define prototypes as the mean output vector over training examples per class. Here, we propose to use hyperspheres as output spaces, with class prototypes defined a priori with large margin separation. We position prototypes through data-independent optimization, with an extension to incorporate priors from class semantics. By doing so, we do not require any prototype updating, we can handle any training size, and the output dimensionality is no longer constrained to the number of classes. Furthermore, we generalize to regression, by optimizing outputs as an interpolation between two prototypes on the hypersphere. Since both tasks are now defined by the same loss function, they can be jointly trained for multi-task problems. Experimentally, we show the benefit of hyperspherical prototype networks for classification, regression, and their combination over other prototype methods, softmax cross-entropy, and mean squared error approaches.

We propose a novel deep learning method for local self-supervised representation learning that does not require labels nor end-to-end backpropagation but exploits the natural order in data instead. Inspired by the observation that biological neural networks appear to learn without backpropagating a global error signal, we split a deep neural network into a stack of gradient-isolated modules. Each module is trained to maximally preserve the information of its inputs using the InfoNCE bound from Oord et al. [2018]. Despite this greedy training, we demonstrate that each module improves upon the output of its predecessor, and that the representations created by the top module yield highly competitive results on downstream classification tasks in the audio and visual domain. The proposal enables optimizing modules asynchronously, allowing large-scale distributed training of very deep neural networks on unlabelled datasets.

We introduce deep scale-spaces (DSS), a generalization of convolutional neural networks, exploiting the scale symmetry structure of conventional image recognition tasks. Put plainly, the class of an image is invariant to the scale at which it is viewed. We construct scale equivariant cross-correlations based on a principled extension of convolutions, grounded in the theory of scale-spaces and semigroups. As a very basic operation, these cross-correlations can be used in almost any modern deep learning architecture in a plug-and-play manner. We demonstrate our networks on the Patch Camelyon and Cityscapes datasets, to prove their utility and perform introspective studies to further understand their properties.

We present a general theory of Group equivariant Convolutional Neural Networks (G-CNNs) on homogeneous spaces such as Euclidean space and the sphere. Feature maps in these networks represent fields on a homogeneous base space, and layers are equivariant maps between spaces of fields. The theory enables a systematic classification of all existing G-CNNs in terms of their symmetry group, base space, and field type. We also answer a fundamental question: what is the most general kind of equivariant linear map between feature spaces (fields) of given types? We show that such maps correspond one-to-one with generalized convolutions with an equivariant kernel, and characterize the space of such kernels.

Behavioral cloning reduces policy learning to supervised learning by training a discriminative model to predict expert actions given observations. Such discriminative models are non-causal: the training procedure is unaware of the causal structure of the interaction between the expert and the environment. We point out that ignoring causality is particularly damaging because of the distributional shift in imitation learning. In particular, it leads to a counter-intuitive "causal misidentification" phenomenon: access to more information can yield worse performance. We investigate how this problem arises, and propose a solution to combat it through targeted interventions---either environment interaction or expert queries---to determine the correct causal model. We show that causal misidentification occurs in several benchmark control domains as well as realistic driving settings, and validate our solution against DAgger and other baselines and ablations.

The big empirical success of group equivariant networks has led in recent years to the sprouting of a great variety of equivariant network architectures. A particular focus has thereby been on rotation and reflection equivariant CNNs for planar images. Here we give a general description of E(2)-equivariant convolutions in the framework of Steerable CNNs. The theory of Steerable CNNs thereby yields constraints on the convolution kernels which depend on group representations describing the transformation laws of feature spaces. We show that these constraints for arbitrary group representations can be reduced to constraints under irreducible representations. A general solution of the kernel space constraint is given for arbitrary representations of the Euclidean group E(2) and its subgroups. We implement a wide range of previously proposed and entirely new equivariant network architectures and extensively compare their performances. E(2)-steerable convolutions are further shown to yield remarkable gains on CIFAR-10, CIFAR-100 and STL-10 when used as drop in replacement for non-equivariant convolutions.

Contains fulltext : 166770.pdf (Publisher’s version ) (Open Access) We developed task-optimized deep neural networks (DNNs) that achieved state-of-the-art performance in different evaluation scenarios for automatic music tagging. These DNNs were subsequently used to probe the neural representations of music. Representational similarity analysis revealed the existence of a representational gradient across the superior temporal gyrus (STG). Anterior STG was shown to be more sensitive to low-level stimulus features encoded in shallow DNN layers whereas posterior STG was shown to be more sensitive to high-level stimulus features encoded in deep DNN layers. 30th Conference on Neural Information Processing Systems (NIPS 2016), Barcelona, Spain, December 5 - 10, 2016, 05 december 2016