According to the United Nations World Water Assessment Programme, every day, 2 million tons of sewage and industrial and agricultural waste are discharged into the worlds water. In order to address this pervasive issue of increasing water pollution, while ensuring that the global population has an efficient, accurate, and low cost method to assess whether the water they drink is contaminated, we propose AquaSight, a novel mobile application that utilizes deep learning methods, specifically Convolutional Neural Networks, for automated water impurity detection. After comprehensive training with a dataset of 105 images representing varying magnitudes of contamination, the deep learning algorithm achieved a 96 percent accuracy and loss of 0.108. Furthermore, the machine learning model uses efficient analysis of the turbidity and transparency levels of water to estimate a particular sample of waters level of contamination. When deployed, the AquaSight system will provide an efficient way for individuals to secure an estimation of water quality, alerting local and national government to take action and potentially saving millions of lives worldwide.

Asynchronous events on the continuous time domain, e.g., social media actions and stock transactions, occur frequently in the world. The ability to recognize occurrence patterns of event sequences is crucial to predict which type of events will happen next and when. A de facto standard mathematical framework to do this is the Hawkes process. In order to enhance expressivity of multivariate Hawkes processes, conventional statistical methods and deep recurrent networks have been employed to modify its intensity function. The former is highly interpretable and requires small size of training data but relies on correct model design while the latter has less dependency on prior knowledge and is more powerful in capturing complicated patterns. We leverage pros and cons of these models and propose a self-attentive Hawkes process (SAHP). The proposed method adapts self-attention to fit the intensity function of Hawkes processes. This design has two benefits: (1) compared with conventional statistical methods, the SAHP is more powerful to identify complicated dependency relationships between temporal events; (2) compared with deep recurrent networks, the self-attention mechanism is able to capture longer historical information, and is more interpretable because the learnt attention weight tensor shows contributions of each historical event. Experiments on four real-world datasets demonstrate the effectiveness of the proposed method.

For many important problems the quantity of interest (or output) is an unknown function of the parameter space (or input), which is a random vector with known statistics. Since the dependence of the output on this random vector is unknown, the challenge is to identify its statistics, using the minimum number of function evaluations. This is a problem that can been seen in the context of active learning or optimal experimental design. We employ Bayesian regression to represent the derived model uncertainty due to finite and small number of input-output pairs. In this context we evaluate existing methods for optimal sample selection, such as model error minimization and mutual information maximization. We show that the commonly employed criteria in the literature do not take into account the output values of the existing input-output pairs. To overcome this deficiency we introduce a new criterion that explicitly takes into account the values of the output for the existing samples and adaptively selects inputs from regions or dimensions of the parameter space which have important contribution to the output. The new method allows for application to a large number of input variables, paving the way for optimal experimental design in very high-dimensions.

A multi-agent system is trialed as a means of crowd-sourcing inexpensive but high quality streams of predictions. Each agent is a microservice embodying statistical models and endowed with economic self-interest. The ability to fork and modify simple agents is granted to a large number of employees in a firm and empirical lessons are reported. We suggest that one plausible trajectory for this project is the creation of a Prediction Web.

SLOPE is a relatively new convex optimization procedure for high-dimensional linear regression via the sorted l1 penalty: the larger the rank of the fitted coefficient, the larger the penalty. This non-separable penalty renders many existing techniques invalid or inconclusive in analyzing the SLOPE solution. In this paper, we develop an asymptotically exact characterization of the SLOPE solution under Gaussian random designs through solving the SLOPE problem using approximate message passing (AMP). This algorithmic approach allows us to approximate the SLOPE solution via the much more amenable AMP iterates. Explicitly, we characterize the asymptotic dynamics of the AMP iterates relying on a recently developed state evolution analysis for non-separable penalties, thereby overcoming the difficulty caused by the sorted l1 penalty. Moreover, we prove that the AMP iterates converge to the SLOPE solution in an asymptotic sense, and numerical simulations show that the convergence is surprisingly fast. Our proof rests on a novel technique that specifically leverages the SLOPE problem. In contrast to prior literature, our work not only yields an asymptotically sharp analysis but also offers an algorithmic, flexible, and constructive approach to understanding the SLOPE problem.

The reactions of the human body to physical exercise, psychophysiological stress and heart diseases are reflected in heart rate variability (HRV). Thus, continuous monitoring of HRV can contribute to determining and predicting issues in well-being and mental health. HRV can be measured in everyday life by consumer wearable devices such as smartwatches which are easily accessible and affordable. However, they are arguably accurate due to the stability of the sensor. We hypothesize a systematic error which is related to the wearer movement. Our evidence builds upon explanatory and predictive modeling: we find a statistically significant correlation between error in HRV measurements and the wearer movement. We show that this error can be minimized by bringing into context additional available sensor information, such as accelerometer data. This work demonstrates our research-in-progress on how neural learning can minimize the error of such smartwatch HRV measurements.

Epidemiologists use a variety of statistical algorithms for the early detection of outbreaks. The practical usefulness of such methods highly depends on the trade-off between the detection rate of outbreaks and the chances of raising a false alarm. Recent research has shown that the use of machine learning for the fusion of multiple statistical algorithms improves outbreak detection. Instead of relying only on the binary output (alarm or no alarm) of the statistical algorithms, we propose to make use of their p-values for training a fusion classifier. In addition, we also show that adding additional features and adapting the labeling of an epidemic period may further improve performance. For comparison and evaluation, a new measure is introduced which captures the performance of an outbreak detection method with respect to a low rate of false alarms more precisely than previous works. Our results on synthetic data show that it is challenging to improve the performance with a trainable fusion method based on machine learning. In particular, the use of a fusion classifier that is only based on binary outputs of the statistical surveillance methods can make the overall performance worse than directly using the underlying algorithms. However, the use of p-values and additional information for the learning is promising, enabling to identify more valuable patterns to detect outbreaks.

Lloyd's $k$-means algorithm is one of the most classical clustering method, which is widely used in data mining or as a data pre-processing procedure. However, due to the thin-tailed property of the Gaussian distribution, $k$-means suffers from relatively poor performance on the heavy-tailed data or outliers. In addition, $k$-means have a relatively weak stability, $i.e.$ its result has a large variance, which reduces the credibility of the model. In this paper, we propose a robust and stable $k$-means variant, the $t$-$k$-means, as well as its fast version in solving the flat clustering problem. Theoretically, we detail the derivations of $t$-$k$-means and analyze its robustness and stability from the aspect of loss function, influence function and the expression of clustering center. A large number of experiments are conducted, which empirically demonstrates that our method has empirical soundness while preserving running efficiency.

Mutual information has been successfully adopted in filter feature-selection methods to assess both the relevancy of a subset of features in predicting the target variable and the redundancy with respect to other variables. However, existing algorithms are mostly heuristic and do not offer any guarantee on the proposed solution. In this paper, we provide novel theoretical results showing that conditional mutual information naturally arises when bounding the ideal regression/classification errors achieved by different subsets of features. Leveraging on these insights, we propose a novel stopping condition for backward and forward greedy methods which ensures that the ideal prediction error using the selected feature subset remains bounded by a user-specified threshold. We provide numerical simulations to support our theoretical claims and compare to common heuristic methods.

Communication is a key bottleneck in distributed training. Recently, an \emph{error-compensated} compression technology was particularly designed for the \emph{centralized} learning and receives huge successes, by showing significant advantages over state-of-the-art compression based methods in saving the communication cost. Since the \emph{decentralized} training has been witnessed to be superior to the traditional \emph{centralized} training in the communication restricted scenario, therefore a natural question to ask is "how to apply the error-compensated technology to the decentralized learning to further reduce the communication cost." However, a trivial extension of compression based centralized training algorithms does not exist for the decentralized scenario. key difference between centralized and decentralized training makes this extension extremely non-trivial. In this paper, we propose an elegant algorithmic design to employ error-compensated stochastic gradient descent for the decentralized scenario, named $\texttt{DeepSqueeze}$. Both the theoretical analysis and the empirical study are provided to show the proposed $\texttt{DeepSqueeze}$ algorithm outperforms the existing compression based decentralized learning algorithms. To the best of our knowledge, this is the first time to apply the error-compensated compression to the decentralized learning.