Gaussian processes (GPs) provide flexible distributions over functions, with inductive biases controlled by a kernel. However, in many applications Gaussian processes can struggle with even moderate input dimensionality. Learning a low dimensional projection can help alleviate this curse of dimensionality, but introduces many trainable hyperparameters, which can be cumbersome, especially in the small data regime. We use additive sums of kernels for GP regression, where each kernel operates on a different random projection of its inputs. Surprisingly, we find that as the number of random projections increases, the predictive performance of this approach quickly converges to the performance of a kernel operating on the original full dimensional inputs, over a wide range of data sets, even if we are projecting into a single dimension. As a consequence, many problems can remarkably be reduced to one dimensional input spaces, without learning a transformation. We prove this convergence and its rate, and additionally propose a deterministic approach that converges more quickly than purely random projections. Moreover, we demonstrate our approach can achieve faster inference and improved predictive accuracy for high-dimensional inputs compared to kernels in the original input space.

Both the Dictionary Learning (DL) and Convolutional Neural Networks (CNN) are powerful image representation learning systems based on different mechanisms and principles, however whether we can seamlessly integrate them to improve the per-formance is noteworthy exploring. To address this issue, we propose a novel generalized end-to-end representation learning architecture, dubbed Convolutional Dictionary Pair Learning Network (CDPL-Net) in this paper, which integrates the learning schemes of the CNN and dictionary pair learning into a unified framework. Generally, the architecture of CDPL-Net includes two convolutional/pooling layers and two dictionary pair learn-ing (DPL) layers in the representation learning module. Besides, it uses two fully-connected layers as the multi-layer perception layer in the nonlinear classification module. In particular, the DPL layer can jointly formulate the discriminative synthesis and analysis representations driven by minimizing the batch based reconstruction error over the flatted feature maps from the convolution/pooling layer. Moreover, DPL layer uses l1-norm on the analysis dictionary so that sparse representation can be delivered, and the embedding process will also be robust to noise. To speed up the training process of DPL layer, the efficient stochastic gradient descent is used. Extensive simulations on real databases show that our CDPL-Net can deliver enhanced performance over other state-of-the-art methods.

ABSTRACT Deep neural networks (DNNs) have achieved excellent performance on several tasks and have been widely applied in both academia and industry. However, DNNs are vulnerable to adversarial machine learning attacks, in which noise is added to the input to change the network output. We have devised an image-processing-based method to detect adversarial images based on our observation that adversarial noise is reduced after applying these operations while the normal images almost remain unaffected. In addition to detection, this method can be used to restore the adversarial images' original labels, which is crucial to restoring the normal functionalities of DNN-based systems. Testing using an adversarial machine learning database we created for generating several types of attack using images from the ImageNet Large Scale Visual Recognition Challenge database demonstrated the efficiency of our proposed method for both detection and correction.

Urban air pollution has been linked to various human health concerns, including cardiopulmonary diseases. Communities who suffer from poor air quality often rely on experts to identify pollution sources due to the lack of accessible tools. Taking this into account, we developed Smell Pittsburgh, a system that enables community members to report odors and track where these odors are frequently concentrated. All smell report data are publicly accessible online. These reports are also sent to the local health department and visualized on a map along with air quality data from monitoring stations. This visualization provides a comprehensive overview of the local pollution landscape. Additionally, with these reports and air quality data, we developed a model to predict upcoming smell events and send push notifications to inform communities. We also applied regression analysis to identify statistically significant effects of push notifications on user engagement. Our evaluation of this system demonstrates that engaging residents in documenting their experiences with pollution odors can help identify local air pollution patterns, and can empower communities to advocate for better air quality. All citizen-contributed smell data are publicly accessible and can be downloaded from https://smellpgh.org.

Consider a reference Markov process with initial distribution $\pi_{0}$ and transition kernels $\{M_{t}\}_{t\in[1:T]}$, for some $T\in\mathbb{N}$. Assume that you are given distribution $\pi_{T}$, which is not equal to the marginal distribution of the reference process at time $T$. In this scenario, Schr\"odinger addressed the problem of identifying the Markov process with initial distribution $\pi_{0}$ and terminal distribution equal to $\pi_{T}$ which is the closest to the reference process in terms of Kullback--Leibler divergence. This special case of the so-called Schr\"odinger bridge problem can be solved using iterative proportional fitting, also known as the Sinkhorn algorithm. We leverage these ideas to develop novel Monte Carlo schemes, termed Schr\"odinger bridge samplers, to approximate a target distribution $\pi$ on $\mathbb{R}^{d}$ and to estimate its normalizing constant. This is achieved by iteratively modifying the transition kernels of the reference Markov chain to obtain a process whose marginal distribution at time $T$ becomes closer to $\pi_T = \pi$, via regression-based approximations of the corresponding iterative proportional fitting recursion. We report preliminary experiments and make connections with other problems arising in the optimal transport, optimal control and physics literatures.

Canonical correlation analysis (CCA) is a popular technique for learning representations that are maximally correlated across multiple views in data. In this paper, we extend the CCA based framework for learning a multiview mixture model. We show that the proposed model and a set of simple heuristics yield improvements over standard CCA, as measured in terms of performance on downstream tasks. Our experimental results show that our correlation-based objective meaningfully generalizes the CCA objective to a mixture of CCA models.

Learning knowledge representation is an increasingly important technology applicable in many domain-specific machine learning problems. We discuss the effectiveness of traditional Link Prediction or Knowledge Graph Completion evaluation protocol when embedding knowledge representation for categorised multi-relational data in the clinical domain. Link prediction uses to split the data into training and evaluation subsets, leading to loss of information along training and harming the knowledge representation model accuracy. We propose a Clustering Evaluation Protocol as a replacement alternative to the traditionally used evaluation tasks. We used embedding models trained by a knowledge embedding approach which has been evaluated with clinical datasets. Experimental results with Pearson and Spearman correlations show strong evidence that the novel proposed evaluation protocol is pottentially able to replace link prediction.

This paper deals with distributed finite-sum optimization for learning over networks in the presence of malicious Byzantine attacks. To cope with such attacks, most resilient approaches so far combine stochastic gradient descent (SGD) with different robust aggregation rules. However, the sizeable SGD-induced stochastic gradient noise makes it challenging to distinguish malicious messages sent by the Byzantine attackers from noisy stochastic gradients sent by the 'honest' workers. This motivates us to reduce the variance of stochastic gradients as a means of robustifying SGD in the presence of Byzantine attacks. To this end, the present work puts forth a Byzantine attack resilient distributed (Byrd-) SAGA approach for learning tasks involving finite-sum optimization over networks. Rather than the mean employed by distributed SAGA, the novel Byrd- SAGA relies on the geometric median to aggregate the corrected stochastic gradients sent by the workers. When less than half of the workers are Byzantine attackers, the robustness of geometric median to outliers enables Byrd-SAGA to attain provably linear convergence to a neighborhood of the optimal solution, with the asymptotic learning error determined by the number of Byzantine workers. Numerical tests corroborate the robustness to various Byzantine attacks, as well as the merits of Byrd- SAGA over Byzantine attack resilient distributed SGD.

-- In this paper, we investigate the unsupervised deep representation learning issue and technically propose a novel framework called Deep Self - representative Concept Factorization Network (DSCF - Net), for clustering deep feature s . To improve the representation and clustering abilities, DSCF - Net explicitl y considers discovering hidden deep semantic features, enhancing the robustness properties of the deep factorization to noise and preserving the local manifold structures of deep features. To discover hidden deep representations, DSCF - Net designs a hierarchical factorization architecture using multiple layers of li near transformations, where the hierarchical representation is performed by formulating the problem as optimizing the basis concepts in each layer to improve the representation indirectly. DSCF - Net also improves the robustness by subspace recovery for spar se error correction firstly and then performs the deep factorization in the recovered visual subspace. To obtain locality - preserving representations, we also present an adaptive deep self - representative weighting strategy by using the coefficient matrix as the adaptive reconstruction weights to keep the locality of representation s . Extensive comparison results with several other related models show that DSCF - Net delivers state - of - the - art performance on several public databases. R epresentation learning from h igh - dimensional complex data is always an important and fundamental problem in the fields of pattern recognition an d data mining [40 - 50 ] .

A brain-computer interface (BCI) system usually needs a long calibration session for each new subject/task to adjust its parameters, which impedes its transition from the laboratory to real-world applications. Domain adaptation, which leverages labeled data from auxiliary subjects/tasks (source domains), has demonstrated its effectiveness in reducing such calibration effort. Currently, most domain adaptation approaches require the source domains to have the same feature space and label space as the target domain, which limits their applications, as the auxiliary data may have different feature spaces and/or different label spaces. This paper considers different set domain adaptation for BCIs, i.e., the source and target domains have different label spaces. We introduce a practical setting of different label sets for BCIs, and propose a novel label alignment (LA) approach to align the source label space with the target label space. It has three desirable properties: 1) LA only needs as few as one labeled sample from each class of the target subject; 2) LA can be used as a preprocessing step before different feature extraction and classification algorithms; and, 3) LA can be integrated with other domain adaptation approaches to achieve even better performance. Experiments on two motor imagery datasets demonstrated the effectiveness of LA.