Tensor factorization is a powerful tool to analyse multi-way data. Compared with traditional multi-linear methods, nonlinear tensor factorization models are capable of capturing more complex relationships in the data. However, they are computationally expensive and may suffer severe learning bias in case of extreme data sparsity. To overcome these limitations, in this paper we propose a distributed, flexible nonlinear tensor factorization model. Our model can effectively avoid the expensive computations and structural restrictions of the Kronecker-product in existing TGP formulations, allowing an arbitrary subset of tensorial entries to be selected to contribute to the training. At the same time, we derive a tractable and tight variational evidence lower bound (ELBO) that enables highly decoupled, parallel computations and high-quality inference. Based on the new bound, we develop a distributed inference algorithm in the MapReduce framework, which is key-value-free and can fully exploit the memory cache mechanism in fast MapReduce systems such as SPARK. Experimental results fully demonstrate the advantages of our method over several state-of-the-art approaches, in terms of both predictive performance and computational efficiency. Moreover, our approach shows a promising potential in the application of Click-Through-Rate (CTR) prediction for online advertising.

Then there are'quantum machine learning algorithms,' developed over the last decade following a breakthrough by Harrow, Hassidim, and Lloyd, which do address problems like clustering, classification, support-vector machines, etc. But these algorithms typically require a bunch of conditions to work: for example, that the data are well-conditioned; that they can be accessed in quantum superposition (for example, using a "quantum RAM") or else computed on the fly; and that the properties of the data one cares about can actually be estimated by measuring the resulting quantum states. And we don't yet know how often those conditions will hold in practical applications---and equally important, in the cases where they do hold, we don't have strong evidence that there couldn't be classical random sampling algorithms with similar performance to the quantum algorithms.

This repository provides a logistic regression implementation in python for our fair classification mechanism introduced in (Zafar et al., 2016). Please cite the paper when using the code. Fair classification corresponds to a scenario where we are learning classifiers from a dataset that is biased towards/against a specific demographic group, yet the classifier predictions are fair and do not show the biases contained in the data. For more details, have a look at Section 2 of our paper. Lets start off by generating a sample dataset where class labels are biased towards a certain group.

K Nearest Neighbor (Knn) is a classification algorithm. It falls under the category of supervised machine learning. It is supervised machine learning because the data set we are using to "train" with contains results (outcomes). It is easier to show you what I mean. This data set contains 42 student test score (Score) and whether or not they were accepted (Accepted) in a college program.

Apache Spark, the open-source cluster computing framework, will soon see a major update with the upcoming release of Spark 2.0. This update promises to be faster than Spark 1.6, thanks to a run-time compiler that generates optimized bytecode. It also promises to be easier for developers to use, with streamlined APIs and a more complete SQL implementation. Spark 2.0 will also include a new "structured streaming" API, which will allow developers to write algorithm for streaming data without having to worry about the fact that streaming data is always incomplete; algorithms written for complete DataFrame objects will work for streams as well. This update also includes some news for R users.

In this challenge, we ask you to invent a new technique for clustering, based on separating hyperplanes. SVM (support vector machines) add many fictitious (dummy) variables and a non-linear mapping (to increase dimensionality and find hyperplanes on transformed variables), thus providing nearly or exact class separation (the purpose of clustering!) when traditional linear clustering fails.

We study the problem of sampling k-bandlimited signals on graphs. We propose two sampling strategies that consist in selecting a small subset of nodes at random. The first strategy is non-adaptive, i.e., independent of the graph structure, and its performance depends on a parameter called the graph coherence. On the contrary, the second strategy is adaptive but yields optimal results. Indeed, no more than O(k log(k)) measurements are sufficient to ensure an accurate and stable recovery of all k-bandlimited signals. This second strategy is based on a careful choice of the sampling distribution, which can be estimated quickly. Then, we propose a computationally efficient decoder to reconstruct k-bandlimited signals from their samples. We prove that it yields accurate reconstructions and that it is also stable to noise. Finally, we conduct several experiments to test these techniques.

We propose an algorithm for detecting patterns exhibited by anomalous clusters in high dimensional discrete data. Unlike most anomaly detection (AD) methods, which detect individual anomalies, our proposed method detects groups (clusters) of anomalies; i.e. sets of points which collectively exhibit abnormal patterns. In many applications this can lead to better understanding of the nature of the atypical behavior and to identifying the sources of the anomalies. Moreover, we consider the case where the atypical patterns exhibit on only a small (salient) subset of the very high dimensional feature space. Individual AD techniques and techniques that detect anomalies using all the features typically fail to detect such anomalies, but our method can detect such instances collectively, discover the shared anomalous patterns exhibited by them, and identify the subsets of salient features. In this paper, we focus on detecting anomalous topics in a batch of text documents, developing our algorithm based on topic models. Results of our experiments show that our method can accurately detect anomalous topics and salient features (words) under each such topic in a synthetic data set and two real-world text corpora and achieves better performance compared to both standard group AD and individual AD techniques. All required code to reproduce our experiments is available from https://github.com/hsoleimani/ATD

Nonlinear independent component analysis (ICA) provides an appealing framework for unsupervised feature learning, but the models proposed so far are not identifiable. Here, we first propose a new intuitive principle of unsupervised deep learning from time series which uses the nonstationary structure of the data. Our learning principle, time-contrastive learning (TCL), finds a representation which allows optimal discrimination of time segments (windows). Surprisingly, we show how TCL can be related to a nonlinear ICA model, when ICA is redefined to include temporal nonstationarities. In particular, we show that TCL combined with linear ICA estimates the nonlinear ICA model up to point-wise transformations of the sources, and this solution is unique --- thus providing the first identifiability result for nonlinear ICA which is rigorous, constructive, as well as very general.

We propose an algorithm, semismooth Newton coordinate descent (SNCD), for the elastic-net penalized Huber loss regression and quantile regression in high dimensional settings. Unlike existing coordinate descent type algorithms, the SNCD updates each regression coefficient and its corresponding subgradient simultaneously in each iteration. It combines the strengths of the coordinate descent and the semismooth Newton algorithm, and effectively solves the computational challenges posed by dimensionality and nonsmoothness. We establish the convergence properties of the algorithm. In addition, we present an adaptive version of the "strong rule" for screening predictors to gain extra efficiency. Through numerical experiments, we demonstrate that the proposed algorithm is very efficient and scalable to ultra-high dimensions. We illustrate the application via a real data example.