Stochastic gradient methods enable learning probabilistic models from large amounts of data. While large step-sizes (learning rates) have shown to be best for least-squares (e.g., Gaussian noise) once combined with parameter averaging, these are not leading to convergent algorithms in general. In this paper, we consider generalized linear models, that is, conditional models based on exponential families. We propose averaging moment parameters instead of natural parameters for constant-step-size stochastic gradient descent. For finite-dimensional models, we show that this can sometimes (and surprisingly) lead to better predictions than the best linear model. For infinite-dimensional models, we show that it always converges to optimal predictions, while averaging natural parameters never does. We illustrate our findings with simulations on synthetic data and classical benchmarks with many observations.

In 2018, at the World Economic Forum in Davos it was presented a new countries' economic performance metric named the Inclusive Development Index (IDI) composed of 12 indicators. The new metric implies that countries might need to realize structural reforms for improving both economic expansion and social inclusion performance. That is why, it is vital for the IDI calculation method to have strong statistical and mathematical basis, so that results are accurate and transparent for public purposes. In the current work, we propose a novel approach for the IDI estimation - the Ranking Relative Principal Component Attributes Network Model (REL-PCANet). The model is based on RELARM and RankNet principles and combines elements of PCA, techniques applied in image recognition and learning to rank mechanisms. Also, we define a new approach for estimation of target probabilities matrix to reflect dynamic changes in countries' inclusive development. Empirical study proved that REL-PCANet ensures reliable and robust scores and rankings, thus is recommended for practical implementation.

Recently, Factorization Machines (FM) has become more and more popular for recommendation systems, due to its effectiveness in finding informative interactions between features. Usually, the weights for the interactions is learnt as a low rank weight matrix, which is formulated as an inner product of two low rank matrices. This low rank can help improve the generalization ability of Factorization Machines. However, to choose the rank properly, it usually needs to run the algorithm for many times using different ranks, which clearly is inefficient for some large-scale datasets. To alleviate this issue, we propose an Adaptive Boosting framework of Factorization Machines (AdaFM), which can adaptively search for proper ranks for different datasets without re-training. Instead of using a fixed rank for FM, the proposed algorithm will adaptively gradually increases its rank according to its performance until the performance does not grow, using boosting strategy. To verify the performance of our proposed framework, we conduct an extensive set of experiments on many real-world datasets. Encouraging empirical results shows that the proposed algorithms are generally more effective than state-of-the-art other Factorization Machines.

Area under ROC (AUC) is an important metric for binary classification and bipartite ranking problems. However, it is difficult to directly optimizing AUC as a learning objective, so most existing algorithms are based on optimizing a surrogate loss to AUC. One significant drawback of these surrogate losses is that they require pairwise comparisons among training data, which leads to slow running time and increasing local storage for online learning. In this work, we describe a new surrogate loss based on a reformulation of the AUC risk, which does not require pairwise comparison but rankings of the predictions. We further show that the ranking operation can be avoided, and the learning objective obtained based on this surrogate enjoys linear complexity in time and storage. We perform experiments to demonstrate the effectiveness of the online and batch algorithms for AUC optimization based on the proposed surrogate loss.

In this paper, we propose a novel supervised learning method that is called Deep Embedding Kernel (DEK). DEK combines the advantages of deep learning and kernel methods in a unified framework. More specifically, DEK is a learnable kernel represented by a newly designed deep architecture. Compared with pre-defined kernels, this kernel can be explicitly trained to map data to an optimized high-level feature space where data may have favorable features toward the application. Compared with typical deep learning using SoftMax or logistic regression as the top layer, DEK is expected to be more generalizable to new data. Experimental results show that DEK has superior performance than typical machine learning methods in identity detection, classification, regression, dimension reduction, and transfer learning.

With the advent of Big Data era, data reduction methods are highly demanded given its ability to simplify huge data, and ease complex learning processes. Concretely, algorithms that are able to filter relevant dimensions from a set of millions are of huge importance. Although effective, these techniques suffer from the "scalability" curse as well. In this work, we propose a distributed feature weighting algorithm, which is able to rank millions of features in parallel using large samples. This method, inspired by the well-known RELIEF algorithm, introduces a novel redundancy elimination measure that provides similar schemes to those based on entropy at a much lower cost. It also allows smooth scale up when more instances are demanded in feature estimations. Empirical tests performed on our method show its estimation ability in manifold huge sets --both in number of features and instances--, as well as its simplified runtime cost (specially, at the redundancy detection step).

A key aspect of a sustainable urban transportation system is the effectiveness of transportation policies. To be effective, a policy has to consider a broad range of elements, such as pollution emission, traffic flow, and human mobility. Due to the complexity and variability of these elements in the urban area, to produce effective policies remains a very challenging task. With the introduction of the smart city paradigm, a widely available amount of data can be generated in the urban spaces. Such data can be a fundamental source of knowledge to improve policies because they can reflect the sustainability issues underlying the city. In this context, we propose an approach to exploit urban positioning data based on stigmergy, a bio-inspired mechanism providing scalar and temporal aggregation of samples. By employing stigmergy, samples in proximity with each other are aggregated into a functional structure called trail. The trail summarizes relevant dynamics in data and allows matching them, providing a measure of their similarity. Moreover, this mechanism can be specialized to unfold specific dynamics. Specifically, we identify high-density urban areas (i.e hotspots), analyze their activity over time, and unfold anomalies. Moreover, by matching activity patterns, a continuous measure of the dissimilarity with respect to the typical activity pattern is provided. This measure can be used by policy makers to evaluate the effect of policies and change them dynamically. As a case study, we analyze taxi trip data gathered in Manhattan from 2013 to 2015.

Machine Learning Practitioners have different personalities. While some of them are "I am an expert in X and X can train on any type of data", where X some algorithm, some others are "Right tool for the right job people". A lot of them also subscribe to "Jack of all trades. Master of one" strategy, where they have one area of deep expertise and know slightly about different fields of Machine Learning. That said, no one can deny the fact that as practicing Data Scientists, we will have to know basics of some common machine learning algorithms, which would help us engage with a new-domain problem we come across.

As learning algorithms are increasingly deployed in markets and other competitive environments, understanding their dynamics is becoming increasingly important. We study the limiting behavior of competitive agents employing gradient-based learning algorithms. Specifically, we introduce a general framework for competitive gradient-based learning that encompasses a wide breadth of learning algorithms including policy gradient reinforcement learning, gradient based bandits, and certain online convex optimization algorithms. We show that unlike the single agent case, gradient learning schemes in competitive settings do not necessarily correspond to gradient flows and, hence, it is possible for limiting behaviors like periodic orbits to exist. We introduce a new class of games, Morse-Smale games, that correspond to gradient-like flows. We provide guarantees that competitive gradient-based learning algorithms (both in the full information and gradient-free settings) avoid linearly unstable critical points (i.e. strict saddle points and unstable limit cycles). Since generic local Nash equilibria are not unstable critical points---that is, in a formal mathematical sense, almost all Nash equilibria are not strict saddles---these results imply that gradient-based learning almost surely does not get stuck at critical points that do not correspond to Nash equilibria. For Morse-Smale games, we show that competitive gradient learning converges to linearly stable cycles (which includes stable Nash equilibria) almost surely. Finally, we specialize these results to commonly used multi-agent learning algorithms and provide illustrative examples that demonstrate the wide range of limiting behaviors competitive gradient learning exhibits.

With a new era of cloud and big data, Database Management Systems (DBMSs) have become more crucial in numerous enterprise business applications in all the industries. Accordingly, the importance of their proactive and preventive maintenance has also increased. However, detecting problems by predefined rules or stochastic modeling has limitations, particularly when analyzing the data on high-dimensional Key Performance Indicators (KPIs) from a DBMS. In recent years, Deep Learning (DL) has opened new opportunities for this complex analysis. In this paper, we present two complementary DL approaches to detect anomalies in SAP HANA. A temporal learning approach is used to detect abnormal patterns based on unlabeled historical data, whereas a spatial learning approach is used to classify known anomalies based on labeled data. We implement a system in SAP HANA integrated with Google TensorFlow. The experimental results with real-world data confirm the effectiveness of the system and models.