Traditional authentication systems use alphanumeric or graphical passwords, or token-based techniques that require "something you know and something you have". The disadvantages of these systems include the risks of forgetfulness, loss, and theft. To address these shortcomings, biometric authentication is rapidly replacing traditional authentication methods and is becoming an everyday part of life. The electrocardiogram (ECG) is one of the most recent traits considered for biometric purposes, and three typical use cases have been described: security checks, hospitals and wearable devices. Here we describe an ECG-based authentication system suitable for security checks and hospital environments. The proposed authentication system will help investigators studying ECG-based biometric authentication techniques to define dataset boundaries and to acquire high-quality training data. We evaluated the performance of the proposed system using a confusion matrix and also by applying the Amang ECG (amgecg) toolbox in MATLAB to investigate two parameters that directly affect the accuracy of authentication: the ECG slicing time (sliding window) and sampling time. Using this approach, we found that accuracy was optimized by using a sliding window of 0.4 s and a sampling time of 37 s.

Retaining premium players is key to the success of free-to-play games, but most of them do not start purchasing right after joining the game. By exploiting the exceptionally rich datasets recorded by modern video games--which provide information on the individual behavior of each and every player--survival analysis techniques can be used to predict what players are more likely to become paying (or even premium) users and when, both in terms of time and game level, the conversion will take place. Here we show that a traditional semi-parametric model (Cox regression), a random survival forest (RSF) technique and a method based on conditional inference survival ensembles all yield very promising results. However, the last approach has the advantage of being able to correct the inherent bias in RSF models by dividing the procedure into two steps: first selecting the best predictor to perform the splitting and then the best split point for that covariate. The proposed conditional inference survival ensembles method could be readily used in operational environments for early identification of premium players and the parts of the game that may prompt them to become paying users. Such knowledge would allow developers to induce their conversion and, more generally, to better understand the needs of their players and provide them with a personalized experience, thereby increasing their engagement and paving the way to higher monetization.

To keep things simple, we will start with running example in which we consider the problem of estimating the price of a house (e.g. in dollars) based on area (e.g. in square feet) and age (e.g. in years). In economics papers, it is common for authors to write out linear models in this format with a gigantic equation that spans multiple lines containing terms for every single feature. For the high-dimensional data that we often address in machine learning, writing out the entire model can be tedious. In these cases, we will find it more convenient to use linear algebra notation. Above, the vector \(\mathbf{x}\) corresponds to a single data point.

Many statistical and machine learning approaches rely on pairwise distances between data points. The choice of distance metric has a fundamental impact on performance of these procedures, raising questions about how to appropriately calculate distances. When data points are real-valued vectors, by far the most common choice is the Euclidean distance. This article is focused on the problem of how to better calculate distances taking into account the intrinsic geometry of the data, assuming data are concentrated near an unknown subspace or manifold. The appropriate geometric distance corresponds to the length of the shortest path along the manifold, which is the geodesic distance. When the manifold is unknown, it is challenging to accurately approximate the geodesic distance. Current algorithms are either highly complex, and hence often impractical to implement, or based on simple local linear approximations and shortest path algorithms that may have inadequate accuracy. We propose a simple and general alternative, which uses pieces of spheres, or spherelets, to locally approximate the unknown subspace and thereby estimate the geodesic distance through paths over spheres. Theory is developed showing lower error for many manifolds. This conclusion is supported through multiple simulation examples and applications to real data sets.

Estimating causal effects for survival outcomes in the high-dimensional setting is an extremely important topic for many biomedical applications as well as areas of social sciences. We propose a new orthogonal score method for treatment effect estimation and inference that results in asymptotically valid confidence intervals assuming only good estimation properties of the hazard outcome model and the conditional probability of treatment. This guarantee allows us to provide valid inference for the conditional treatment effect under the high-dimensional additive hazards model under considerably more generality than existing approaches. In addition, we develop a new Hazards Difference (HDi), estimator. We showcase that our approach has double-robustness properties in high dimensions: with cross-fitting, the HDi estimate is consistent under a wide variety of treatment assignment models; the HDi estimate is also consistent when the hazards model is misspecified and instead the true data generating mechanism follows a partially linear additive hazards model. We further develop a novel sparsity doubly robust result, where either the outcome or the treatment model can be a fully dense high-dimensional model. We apply our methods to study the treatment effect of radical prostatectomy versus conservative management for prostate cancer patients using the SEER-Medicare Linked Data.

Time series forecasting is an important problem across many domains, including predictions of solar plant energy output, electricity consumption, and traffic jam situation. In this paper, we propose to tackle such forecasting problem with Transformer. Although impressed by its performance in our preliminary study, we found its two major weaknesses: (1) locality-agnostics: the point-wise dot-product self attention in canonical Transformer architecture is insensitive to local context, which can make the model prone to anomalies in time series; (2) memory bottleneck: space complexity of canonical Transformer grows quadratically with sequence length $L$, making modeling long time series infeasible. In order to solve these two issues, we first propose convolutional self attention by producing queries and keys with causal convolution so that local context can be better incorporated into attention mechanism. Then, we propose LogSparse Transformer with only $O(L(\log L)^{2})$ memory cost, improving the time series forecasting in finer granularity under constrained memory budget. Our experiments on both synthetic data and real-world datasets show that it compares favorably to the state-of-the-art.

We present a detailed analysis of the class of regression decision tree algorithms which employ a regulized piecewise-linear node-splitting criterion and have regularized linear models at the leaves. From a theoretic standpoint, based on Rademacher complexity framework, we present new high-probability upper bounds for the generalization error for the proposed classes of regularized regression decision tree algorithms, including LASSO-type, and $\ell_{2}$ regularization for linear models at the leaves. Theoretical result are further extended by considering a general type of variable selection procedure. Furthermore, in our work we demonstrate that the class of piecewise-linear regression trees is not only numerically stable but can be made tractable via an algorithmic implementation, presented herein, as well as with the help of modern GPU technology. Empirically, we present results on multiple datasets which highlight the strengths and potential pitfalls, of the proposed tree algorithms compared to baselines which grow trees based on piecewise constant models.

Census data provide detailed information about population characteristics at a coarse resolution. Nevertheless, fine-grained, high-resolution mappings of population counts are increasingly needed to characterize population dynamics and to assess the consequences of climate shocks, natural disasters, investments in infrastructure, development policies, etc. Dissagregating these census is a complex machine learning, and multiple solutions have been proposed in past research. We propose in this paper to view the problem in the context of the aggregate learning paradigm, where the output value for all training points is not known, but where it is only known for aggregates of the points (i.e. in this context, for regions of pixels where a census is available). We demonstrate with a very simple and interpretable model that this method is on par, and even outperforms on some metrics, the state-of-the-art, despite its simplicity.

As one of the most popular linear subspace learning methods, the Linear Discriminant Analysis (LDA) method has been widely studied in machine learning community and applied to many scientific applications. Traditional LDA minimizes the ratio of squared L2-norms, which is sensitive to outliers. In recent research, many L1-norm based robust Principle Component Analysis methods were proposed to improve the robustness to outliers. However, due to the difficulty of L1-norm ratio optimization, so far there is no existing work to utilize sparsity-inducing norms for LDA objective. In this paper, we propose a novel robust linear discriminant analysis method based on the L1,2-norm ratio minimization. Minimizing the L1,2-norm ratio is a much more challenging problem than the traditional methods, and there is no existing optimization algorithm to solve such non-smooth terms ratio problem. We derive a new efficient algorithm to solve this challenging problem, and provide a theoretical analysis on the convergence of our algorithm. The proposed algorithm is easy to implement, and converges fast in practice. Extensive experiments on both synthetic data and nine real benchmark data sets show the effectiveness of the proposed robust LDA method.

We deal with the \textit{selective classification} problem (supervised-learning problem with a rejection option), where we want to achieve the best performance at a certain level of coverage of the data. We transform the original $m$-class classification problem to $(m+1)$-class where the $(m+1)$-th class represents the model abstaining from making a prediction due to uncertainty. Inspired by portfolio theory, we propose a loss function for the selective classification problem based on the doubling rate of gambling. We show that minimizing this loss function has a natural interpretation as maximizing the return of a \textit{horse race}, where a player aims to balance between betting on an outcome (making a prediction) when confident and reserving one's winnings (abstaining) when not confident. This loss function allows us to train neural networks and characterize the uncertainty of prediction in an end-to-end fashion. In comparison with previous methods, our method requires almost no modification to the model inference algorithm or neural architecture. Experimentally, we show that our method can identify both uncertain and outlier data points, and achieves strong results on SVHN and CIFAR10 at various coverages of the data.