This note is a response to [7] in which it is claimed that [13, Proposition 11] is false. We demonstrate here that this assertion in [7] is false, and is based on a misreading of the notion of set membership in [13, Proposition 11]. We maintain that [13, Proposition 11] is true. Based on the empirical risk principle, one should minimize at training time the loss that one wishes to evaluate at test time [10]. In [12, 13], we have studied the construction of surrogates for loss functions that are submodular with respect to the set of mispredictions.

We extend the Nystr\"om method for low-rank approximation of positive definite Mercer kernels to approximation of indefinite kernel matrices. Our result is the first derivation of the approach that does not require the positive definiteness of the kernel function. Building on this result, we then devise highly scalable methods for learning in reproducing kernel Kre\u{\i}n spaces. The main motivation for our work comes from problems with structured representations (e.g., graphs, strings, time-series), where it is relatively easy to devise a pairwise (dis)similarity function based on intuition/knowledge of a domain expert. Such pairwise functions are typically not positive definite and it is often well beyond the expertise of practitioners to verify this condition. The proposed large scale approaches for learning in reproducing kernel Kre\u{\i}n spaces provide principled and theoretically well-founded means to tackle this class of problems. The effectiveness of the approaches is evaluated empirically using kernels defined on structured and vectorial data representations.

This document serves to complement our website which was developed with the aim of exposing the students to Gaussian Processes (GPs). GPs are non-parametric Bayesian regression models that are largely used by statisticians and geospatial data scientists for modeling spatial data. Several open source libraries spanning from Matlab [1], Python [2], R [3] etc., are already available for simple plug-and-use. The objective of this handout and in turn the website was to allow the users to develop stand-alone GPs in Python by relying on minimal external dependencies. To this end, we only use the default python modules and assist the users in developing their own GPs from scratch giving them an in-depth knowledge of what goes on under the hood. The module covers GP inference using maximum likelihood estimation (MLE) and gives examples of 1D (dummy) spatial data.

T ensor Ring Decomposition with Rank Minimization on Latent Space: An Efficient Approach for T ensor Completion Anonymous Authors Affiliation Address email Abstract In tensor completion tasks, the traditional low-rank tensor decomposition models suffer from laborious model selection problem due to high model sensitivity. Especially for tensor ring (TR) decomposition, the number of model possibility grows exponentially with the tensor order, which makes it rather challenging to find the optimal TR decomposition. In this paper, by exploiting the low-rank structure on TR latent space, we propose a novel tensor completion method, which is robust to model selection. In contrast to imposing low-rank constraint on the data space, we introduce nuclear norm regularization on the latent TR factors, resulting in that the optimization step using singular value decomposition (SVD) can be performed at a much smaller scale. By leveraging the alternating direction method of multipliers (ADMM) scheme, the latent TR factors with optimal rank and the recovered tensor can be obtained simultaneously. Our proposed algorithm effectively alleviates the burden of TR-rank selection, therefore the computational cost is greatly reduced. The extensive experimental results on synthetic data and real-world data demonstrate the superior high performance and efficiency of the proposed approach against the state-of-the-art algorithms. Introduction Tensor decomposition aims to find the latent factors of tensor-valued data (i.e. the generalization of multidimensional arrays), thereby casting large-scale tensors into a multilinear tensor latent space of low-dimensionality (very few degrees of freedom designated by the rank).

Streaming tensor factorization is a powerful tool for processing high-volume and multi-way temporal data in Internet networks, recommender systems and image/video data analysis. Existing streaming tensor factorization algorithms rely on least-squares data fitting and they do not possess a mechanism for tensor rank determination. This leaves them susceptible to outliers and vulnerable to over-fitting. This paper presents a Bayesian robust streaming tensor factorization model to identify sparse outliers, automatically determine the underlying tensor rank and accurately fit low-rank structure. We implement our model in Matlab and compare it with existing algorithms on tensor datasets generated from dynamic MRI and Internet traffic.

As an important tool in security, the intrusion detection system bears the responsibility of the defense to network attacks performed by malicious traffic. Nowadays, with the help of machine learning algorithms, the intrusion detection system develops rapidly. However, the robustness of this system is questionable when it faces the adversarial attacks. To improve the detection system, more potential attack approaches should be researched. In this paper, a framework of the generative adversarial networks, IDSGAN, is proposed to generate the adversarial attacks, which can deceive and evade the intrusion detection system. Considering that the internal structure of the detection system is unknown to attackers, adversarial attack examples perform the black-box attacks against the detection system. IDSGAN leverages a generator to transform original malicious traffic into adversarial malicious traffic. A discriminator classifies traffic examples and simulates the black-box detection system. More significantly, we only modify part of the attacks' nonfunctional features to guarantee the validity of the intrusion. Based on the dataset NSL-KDD, the feasibility of the model is demonstrated to attack many detection systems with different attacks and the excellent results are achieved. Moreover, the robustness of IDSGAN is verified by changing the amount of the unmodified features.

This paper proposes a tutorial on the Data Clustering technique using the Particle Swarm Optimization approach. Following the work proposed by Merwe et al. [1] here we present an in-deep analysis of the algorithm together with a Matlab implementation and a short tutorial that explains how to modify the proposed implementation and the effect of the parameters of the original algorithm. Moreover, we provide a comparison against the results obtained using the well known K-Means approach. All the source code presented in this paper is publicly available under the GPL-v2 license.

Recent progress in deep learning is revolutionizing the healthcare domain including providing solutions to medication recommendations, especially recommending medication combination for patients with complex health conditions. Existing approaches either do not customize based on patient health history, or ignore existing knowledge on drug-drug interactions (DDI) that might lead to adverse outcomes. To fill this gap, we propose the Graph Augmented Memory Networks (GAMENet), which integrates the drug-drug interactions knowledge graph by a memory module implemented as a graph convolutional networks, and models longitudinal patient records as the query. It is trained end-to-end to provide safe and personalized recommendation of medication combination. We demonstrate the effectiveness and safety of GAMENet by comparing with several state-of-the-art methods on real EHR data. GAMENet outperformed all baselines in all effectiveness measures, and also achieved 3.60% DDI rate reduction from existing EHR data.

Feature-mapping with deep neural networks is commonly used for single-channel speech enhancement, in which a feature-mapping network directly transforms the noisy features to the corresponding enhanced ones and is trained to minimize the mean square errors between the enhanced and clean features. In this paper, we propose an adversarial feature-mapping (AFM) method for speech enhancement which advances the feature-mapping approach with adversarial learning. An additional discriminator network is introduced to distinguish the enhanced features from the real clean ones. The two networks are jointly optimized to minimize the feature-mapping loss and simultaneously mini-maximize the discrimination loss. The distribution of the enhanced features is further pushed towards that of the clean features through this adversarial multi-task training. To achieve better performance on ASR task, senone-aware (SA) AFM is further proposed in which an acoustic model network is jointly trained with the feature-mapping and discriminator networks to optimize the senone classification loss in addition to the AFM losses. Evaluated on the CHiME-3 dataset, the proposed AFM achieves 16.95% and 5.27% relative word error rate (WER) improvements over the real noisy data and the feature-mapping baseline respectively and the SA-AFM achieves 9.85% relative WER improvement over the multi-conditional acoustic model.

Complex systems, such as airplanes, cars, or financial markets, produce multivariate time series data consisting of system observations over a period of time. Such data can be interpreted as a sequence of segments, where each segment is associated with a certain state of the system. An important problem in this domain is to identify repeated sequences of states, known as motifs. Such motifs correspond to complex behaviors that capture common sequences of state transitions. For example, a motif of "making a turn" might manifest in sensor data as a sequence of states: slowing down, turning the wheel, and then speeding back up. However, discovering these motifs is challenging, because the individual states are unknown and need to be learned from the noisy time series. Simultaneously, the time series also needs to be precisely segmented and each segment needs to be associated with a state. Here we develop context-aware segmentation and clustering (CASC), a method for discovering common motifs in time series data. We formulate the problem of motif discovery as a large optimization problem, which we then solve using a greedy alternating minimization-based approach. CASC performs well in the presence of noise in the input data and is scalable to very large datasets. Furthermore, CASC leverages common motifs to more robustly segment the time series and assign segments to states. Experiments on synthetic data show that CASC outperforms state-of-the-art baselines by up to 38.2%, and two case studies demonstrate how our approach discovers insightful motifs in real-world time series data.