We introduce the probabilistic sequential matrix factorization (PSMF) method for factorizing time-varying and non-stationary datasets consisting of high-dimensional time-series. In particular, we consider nonlinear-Gaussian state-space models in which sequential approximate inference results in the factorization of a data matrix into a dictionary and time-varying coefficients with (possibly nonlinear) Markovian dependencies. The assumed Markovian structure on the coefficients enables us to encode temporal dependencies into a low-dimensional feature space. The proposed inference method is solely based on an approximate extended Kalman filtering scheme which makes the resulting method particularly efficient. The PSMF can account for temporal nonlinearities and, more importantly, can be used to calibrate and estimate generic differentiable nonlinear subspace models. We show that the PSMF can be used in multiple contexts: modelling time series with a periodic subspace, robustifying changepoint detection methods, and imputing missing-data in high-dimensional time-series of air pollutants measured across London.

Effective features can improve the performance of a model, which can thus help us understand the characteristics and underlying structure of complex data. Previous feature selection methods usually cannot keep more local structure information. To address the defects previously mentioned, we propose a novel supervised orthogonal least square regression model with feature weighting for feature selection. The optimization problem of the objection function can be solved by employing generalized power iteration (GPI) and augmented Lagrangian multiplier (ALM) methods. Experimental results show that the proposed method can more effectively reduce the feature dimensionality and obtain better classification results than traditional feature selection methods. The convergence of our iterative method is proved as well. Consequently, the effectiveness and superiority of the proposed method are verified both theoretically and experimentally.

We propose a new forecasting method for predicting load demand and generation scheduling. Accurate week-long forecasting of load demand and optimal power generation is critical for efficient operation of power grid systems. In this work, we use a synthetic data set describing a power grid with 700 buses and 134 generators over a 365-days period with data synthetically generated at an hourly rate. The proposed approach for week-long forecasting is based on the Gaussian process regression (GPR) method, with prior covariance matrices of the quantities of interest (QoI) computed from ensembles formed by up to twenty preceding weeks of QoI observations. Then, we use these covariances within the GPR framework to forecast the QoIs for the following week. We demonstrate that the the proposed ensemble GPR (EGPR) method is capable of accurately forecasting weekly total load demand and power generation profiles. The EGPR method is shown to outperform traditional forecasting methods including the standard GPR and autoregressive integrated moving average (ARIMA) methods.

We present Natural Gradient Boosting (NGBoost), an algorithm which brings probabilistic prediction capability to gradient boosting in a generic way. Predictive uncertainty estimation is crucial in many applications such as healthcare and weather forecasting. Probabilistic prediction, which is the approach where the model outputs a full probability distribution over the entire outcome space, is a natural way to quantify those uncertainties. Gradient Boosting Machines have been widely successful in prediction tasks on structured input data, but a simple boosting solution for probabilistic prediction of real valued outputs is yet to be made. NGBoost is a gradient boosting approach which uses the \emph{Natural Gradient} to address technical challenges that makes generic probabilistic prediction hard with existing gradient boosting methods. Our approach is modular with respect to the choice of base learner, probability distribution, and scoring rule. We show empirically on several regression datasets that NGBoost provides competitive predictive performance of both uncertainty estimates and traditional metrics.

Federated learning (FL) provides a communication-efficient approach to solve machine learning problems concerning distributed data, without sending raw data to a central server. However, existing works on FL only utilize first-order gradient descent (GD) and do not consider the preceding iterations to gradient update which can potentially accelerate convergence. In this paper, we consider momentum term which relates to the last iteration. The proposed momentum federated learning (MFL) uses momentum gradient descent (MGD) in the local update step of FL system. We establish global convergence properties of MFL and derive an upper bound on MFL convergence rate. Comparing the upper bounds on MFL and FL convergence rate, we provide conditions in which MFL accelerates the convergence. For different machine learning models, the convergence performance of MFL is evaluated based on experiments with MNIST dataset. Simulation results comfirm that MFL is globally convergent and further reveal significant convergence improvement over FL.

Jointly quantifying the contribution of the learning algorithm and training dataGal Yona Amirata Ghorbani James Zou Weizmann Institute Stanford University Stanford University Abstract A fancy learning algorithm A outperforms a baseline method B when they are both trained on the same data. Should A get all of the credit for the improved performance or does the training data also deserve some credit? When deployed in a new setting from a different domain, however, A makes more mistakes than B . How much of the blame should go to the learning algorithm or the training data? Such questions are becoming increasingly important and prevalent as we aim to make ML more accountable. Their answers would also help us allocate resources between algorithm design and data collection. In this paper, we formalize these questions and provide a principled Extended Shapley framework to jointly quantify the contribution of the learning algorithm and training data. Extended Shapley uniquely satisfies several natural properties that ensure equitable treatment of data and algorithm. Through experiments and theoretical analysis, we demonstrate that Extended Shapley has several important applications: 1) it provides a new metric of ML performance improvement that disentangles the influence of the data regime and the algorithm; 2) it facilitates ML accountability by properly assigning responsibility for mistakes; 3) it provides more robustness to manipulation by the ML designer. Introduction In machine learning (ML), the standard way to evaluate a new learning algorithm A is to compare its performance with the performance of a baseline algorithm B, when A and B are trained on the same dataset D . For example, if A and B achieves 0.9 and 0.7 accuracy, then papers typically report that A is better than B by 0.2. Implicit in this ubiquitous practice is the assumption that A itself is solely responsible for all of the difference in performance.

Testing two potentially multivariate variables for statistical dependence on the basis finite samples is a fundamental statistical challenge. Here we explore a family of tests that adapt to the complexity of the relationship between the variables, promising robust power across scenarios. Building on the distance correlation, we introduce a family of adaptive independence criteria based on nonlinear monotonic transformations of distances. We show that these criteria, like the distance correlation and RKHS-based criteria, provide dependence indicators. We propose a class of adaptive (multi-threshold) test statistics, which form the basis for permutation tests. These tests empirically outperform some of the established tests in average and worst-case statistical sensitivity across a range of univariate and multivariate relationships and might deserve further exploration.

Many methods exist for function optimization, such as randomly sampling the variable search space, called random search, or systematically evaluating samples in a grid across the search space, called grid search. More principled methods are able to learn from sampling the space so that future samples are directed toward the parts of the search space that are most likely to contain the extrema. A directed approach to global optimization that uses probability is called Bayesian Optimization. Take my free 7-day email crash course now (with sample code). Click to sign-up and also get a free PDF Ebook version of the course.

The article explains the SVM algorithm in an easy way. Machine Learning is considered as a subfield of Artificial Intelligence and it is concerned with the development of techniques and methods which enable the computer to learn. In simple terms development of algorithms which enable the machine to learn and perform tasks and activities. Over a period of time, many techniques and methodologies were developed for machine learning tasks. In this article, we are going to learn almost everything about one such supervised machine learning algorithm which can be used for both classification and regression(SVR) i.e.

Airbnb is an online-based marketing company that connects people looking for accommodation (Airbnb guests) to people looking to rent their properties (Airbnb hosts) on a short-term or long-term basis. The rentals properties includes apartments (dominant), homes, boats, and whole lot more. Since its inception in 2008, Airbnb has steadily risen in terms of revenue growth and its range of service provisions. As of 2019, there 150 million users of Airbnb services in 191 countries, making it a major disruptor of the traditional hospitality industry (this is akin to how Uber and other emerging transportation services have disrupted the traditional intra-city transportation services). Airbnb generates revenue by charging its guests and hosts fees for arranging stays: hosts are charged 3% of the value of the booking, while guests are charged 6%-12% per the nature of the booking.