Market Basket Analysis (MBA) is a popular technique to identify associations between products, which is crucial for business decision making. Previous studies typically adopt conventional frequent itemset mining algorithms to perform MBA. However, they generally fail to uncover rarely occurring associations among the products at their most granular level. Also, they have limited ability to capture temporal dynamics in associations between products. Hence, we propose OMBA, a novel representation learning technique for Online Market Basket Analysis. OMBA jointly learns representations for products and users such that they preserve the temporal dynamics of product-to-product and user-to-product associations. Subsequently, OMBA proposes a scalable yet effective online method to generate products' associations using their representations. Our extensive experiments on three real-world datasets show that OMBA outperforms state-of-the-art methods by as much as 21%, while emphasizing rarely occurring strong associations and effectively capturing temporal changes in associations.

Kernel methods provide an elegant and principled approach to nonparametric learning, but so far could hardly be used in large scale problems, since na\"ive implementations scale poorly with data size. Recent advances have shown the benefits of a number of algorithmic ideas, for example combining optimization, numerical linear algebra and random projections. Here, we push these efforts further to develop and test a solver that takes full advantage of GPU hardware. Towards this end, we designed a preconditioned gradient solver for kernel methods exploiting both GPU acceleration and parallelization with multiple GPUs, implementing out-of-core variants of common linear algebra operations to guarantee optimal hardware utilization. Further, we optimize the numerical precision of different operations and maximize efficiency of matrix-vector multiplications. As a result we can experimentally show dramatic speedups on datasets with billions of points, while still guaranteeing state of the art performance. Additionally, we make our software available as an easy to use library.

Generative Adversarial Network(GAN) provides a good generative framework to produce realistic samples, but suffers from two recognized issues as mode collapse and unstable training. In this work, we propose to employ explicit manifold learning as prior to alleviate mode collapse and stabilize training of GAN. Since the basic assumption of conventional manifold learning fails in case of sparse and uneven data distribution, we introduce a new target, Minimum Manifold Coding (MMC), for manifold learning to encourage simple and unfolded manifold. In essence, MMC is the general case of the shortest Hamiltonian Path problem and pursues manifold with minimum Riemann volume. Using the standardized code from MMC as prior, GAN is guaranteed to recover a simple and unfolded manifold covering all the training data. Our experiments on both the toy data and real datasets show the effectiveness of MMCGAN in alleviating mode collapse, stabilizing training, and improving the quality of generated samples.

Due to their high computational efficiency on a continuous space, gradient optimization methods have shown great potential in the neural architecture search (NAS) domain. The mapping of network representation from the discrete space to a latent space is the key to discovering novel architectures, however, existing gradient-based methods fail to fully characterize the networks. In this paper, we propose an efficient NAS approach to optimize network architectures in a continuous space, where the latent space is built upon variational autoencoder (VAE) and graph neural networks (GNN). The framework jointly learns four components: the encoder, the performance predictor, the complexity predictor and the decoder in an end-to-end manner. The encoder and the decoder belong to a graph VAE, mapping architectures between continuous representations and network architectures. The predictors are two regression models, fitting the performance and computational complexity, respectively. Those predictors ensure the discovered architectures characterize both excellent performance and high computational efficiency. Extensive experiments demonstrate our framework not only generates appropriate continuous representations but also discovers powerful neural architectures.

Learning the distribution of observed data is a basic task in unsupervised learning which has been studied for decades. The recently-introduced concept of Generative Adversarial Networks (GANs) [1] has demonstrated great success in various distribution learning tasks. Unlike the traditional maximum-likelihood-based approaches, GANs learn the distribution of observed data through a zero-sum game between two machine players, a generator G mimicking the true distribution of data and a discriminator D distinguishing the generator's produced samples from real data points. This zero-sum game is typically formulated through a minimax optimization problem where G and D optimize a minimax objective quantifying how dissimilar G's generated samples and real training samples are. In GAN minimax optimization problems, the generator and discriminator functions are commonly chosen as two deep neural networks (DNNs). Leveraging the expressive power of DNNs, GANs have achieved state-of-the-art performance in learning complex distributions of image data [2, 3, 4]. This success, however, is achieved at the cost of their notoriously difficult training procedure which has introduced several challenges to the machine learning community. Addressing these challenges requires a deeper theoretical understanding of GANs, including their approximation, generalization, and optimization properties. Specifically, GANs have been frequently observed to fail in learning multi-modal distributions [5].

We consider the problem of estimating confidence intervals for the mean of a random variable, where the goal is to produce the smallest possible interval for a given number of samples. While minimax optimal algorithms are known for this problem in the general case, improved performance is possible under additional assumptions. In particular, we design an estimation algorithm to take advantage of side information in the form of a control variate, leveraging order statistics. Under certain conditions on the quality of the control variates, we show improved asymptotic efficiency compared to existing estimation algorithms. Empirically, we demonstrate superior performance on several real world surveying and estimation tasks where we use the output of regression models as the control variates.

While the identification of nonlinear dynamical systems is a fundamental building block of model-based reinforcement learning and feedback control, its sample complexity is only understood for systems that either have discrete states and actions or for systems that can be identified from data generated by i.i.d. random inputs. Nonetheless, many interesting dynamical systems have continuous states and actions and can only be identified through a judicious choice of inputs. Motivated by practical settings, we study a class of nonlinear dynamical systems whose state transitions depend linearly on a known feature embedding of state-action pairs. To estimate such systems in finite time identification methods must explore all directions in feature space. We propose an active learning approach that achieves this by repeating three steps: trajectory planning, trajectory tracking, and re-estimation of the system from all available data. We show that our method estimates nonlinear dynamical systems at a parametric rate, similar to the statistical rate of standard linear regression.

A convex optimization model predicts an output from an input by solving a convex optimization problem. The class of convex optimization models is large, and includes as special cases many well-known models like linear and logistic regression. We propose a heuristic for learning the parameters in a convex optimization model given a dataset of input-output pairs, using recently developed methods for differentiating the solution of a convex optimization problem with respect to its parameters. We describe three general classes of convex optimization models, maximum a posteriori (MAP) models, utility maximization models, and agent models, and present a numerical experiment for each.

Can I become a data scientist with little or no math background? What essential math skills are important in data science? There are so many good packages that can be used for building predictive models or for producing data visualizations. Thanks to these packages, anyone can build a model or produce a data visualization. However, very solid background knowledge in mathematics is essential for fine-tuning your models to produce reliable models with optimal performance.

With rapid advancements in machine learning (ML) techniques over the past decade, intelligent decision-making and prediction systems are poised to transform productivity and lead to significant economic gains. A study conducted by PwC Global concludes that by the end of this decade, the total positive impact of artificial intelligence (AI) on the global economy could be above $15 trillion, driven mostly by enhancements in consumer products. To make that happen, however, businesses must make strategic investments in the type of technology that moves AI projects into production (productionizing) and helps customers deploy them. Unfortunately, PwC's survey reveals the percentage of executives planning to deploy AI has gone down from 20 percent a year ago to only 4 percent at the beginning of 2020. The primary reason for this decrease is the gap between the growing volume of data and data-driven modeling capabilities, and the necessary skills and toolsets.