In this paper we propose a modified version of the simulated annealing algorithm for solving a stochastic global optimization problem. More precisely, we address the problem of finding a global minimizer of a function with noisy evaluations. We provide a rate of convergence and its optimized parametrization to ensure a minimal number of evaluations for a given accuracy and a confidence level close to 1. This work is completed with a set of numerical experimentations and assesses the practical performance both on benchmark test cases and on real world examples.

The composition of multiple Gaussian Processes as a Deep Gaussian Process (DGP) enables a deep probabilistic nonparametric approach to flexibly tackle complex machine learning problems with sound quantification of uncertainty. Existing inference approaches for DGP models have limited scalability and are notoriously cumbersome to construct. In this work, we introduce a novel formulation of DGPs based on random feature expansions that we train using stochastic variational inference. This yields a practical learning framework which significantly advances the state-of-the-art in inference for DGPs, and enables accurate quantification of uncertainty. We extensively showcase the scalability and performance of our proposal on several datasets with up to 8 million observations, and various DGP architectures with up to 30 hidden layers.

Multivariate clustering in astrophysics is a recent development justified by the bigger and bigger surveys of the sky. The phylogenetic approach is probably the most unexpected technique that has appeared for the unsupervised classification of galaxies, stellar populations or globular clusters. On one side, this is a somewhat natural way of classifying astrophysical entities which are all evolving objects. On the other side, several conceptual and practical difficulties arize, such as the hierarchical representation of the astrophysical diversity, the continuous nature of the parameters, and the adequation of the result to the usual practice for the physical interpretation. Most of these have now been solved through the studies of limited samples of stellar clusters and galaxies. Up to now, only the Maximum Parsimony (cladistics) has been used since it is the simplest and most general phylogenetic technique. Probabilistic and network approaches are obvious extensions that should be explored in the future.

The Allstate Claims Severity recruiting competition ran on Kaggle from October to December 2016. As Kaggle's most popular recruiting competitions to-date, it attracted over 3,000 entrants who competed to predict the loss value associated with Allstate insurance claims. In this interview, Alexey Noskov walks us through how he came in second place by creating features based on distance from cluster centroids and applying newfound intuitions for (hyper)-parameter tuning. Along the way, he provides details on his favorite tips and tricks including lots of feature engineering and implementing a custom objective function for XGBoost. I have MSc in computer science and work as a software engineer at Evil Martians.

We present an asymptotic criterion to determine the optimal number of clusters in k-means. We consider k-means as data compression, and propose to adopt the number of clusters that minimizes the estimated description length after compression. Here we report two types of compression ratio based on two ways to quantify the description length of data after compression. This approach further offers a way to evaluate whether clusters obtained with k-means have a hierarchical structure by examining whether multi-stage compression can further reduce the description length. We applied our criteria to determine the number of clusters to synthetic data and empirical neuroimaging data to observe the behavior of the criteria across different types of data set and suitability of the two types of criteria for different datasets. We found that our method can offer reasonable clustering results that are useful for dimension reduction. While our numerical results revealed dependency of our criteria on the various aspects of dataset such as the dimensionality, the description length approach proposed here provides a useful guidance to determine the number of clusters in a principled manner when underlying properties of the data are unknown and only inferred from observation of data.

Discrimination-aware classification is receiving an increasing attention in the data mining and machine learning fields. The data preprocessing methods for constructing a discrimination-free classifier remove discrimination from the training data, and learn the classifier from the cleaned data. However, there lacks of a theoretical guarantee for the performance of these methods. In this paper, we fill this theoretical gap by mathematically bounding the probability that the discrimination in predictions is within a given interval in terms of the given training data and classifier. In our analysis, we adopt the causal model for modeling the mechanisms in data generation, and formally defining discrimination in the population, in a dataset, and in the prediction. The theoretical results show that the fundamental assumption made by the data preprocessing methods is not correct. Finally, we develop a framework for constructing a discrimination-free classifier with a theoretical guarantee.

We consider object recognition in the context of lifelong learning, where a robotic agent learns to discriminate between a growing number of object classes as it accumulates experience about the environment. We propose an incremental variant of the Regularized Least Squares for Classification (RLSC) algorithm, and exploit its structure to seamlessly add new classes to the learned model. The presented algorithm addresses the problem of having an unbalanced proportion of training examples per class, which occurs when new objects are presented to the system for the first time. We evaluate our algorithm on both a machine learning benchmark dataset and two challenging object recognition tasks in a robotic setting. Empirical evidence shows that our approach achieves comparable or higher classification performance than its batch counterpart when classes are unbalanced, while being significantly faster.

Data-target pairing is an important step towards multi-target localization for the intelligent operation of unmanned systems. Target localization plays a crucial role in numerous applications, such as search, and rescue missions, traffic management and surveillance. The objective of this paper is to present an innovative target location learning approach, where numerous machine learning approaches, including K-means clustering and supported vector machines (SVM), are used to learn the data pattern across a list of spatially distributed sensors. To enable the accurate data association from different sensors for accurate target localization, appropriate data pre-processing is essential, which is then followed by the application of different machine learning algorithms to appropriately group data from different sensors for the accurate localization of multiple targets. Through simulation examples, the performance of these machine learning algorithms is quantified and compared.

Graphlets are induced subgraphs of a large network and are important for understanding and modeling complex networks. Despite their practical importance, graphlets have been severely limited to applications and domains with relatively small graphs. Most previous work has focused on exact algorithms, however, it is often too expensive to compute graphlets exactly in massive networks with billions of edges, and finding an approximate count is usually sufficient for many applications. In this work, we propose an unbiased graphlet estimation framework that is (a) fast with significant speedups compared to the state-of-the-art, (b) parallel with nearly linear-speedups, (c) accurate with <1% relative error, (d) scalable and space-efficient for massive networks with billions of edges, and (e) flexible for a variety of real-world settings, as well as estimating macro and micro-level graphlet statistics (e.g., counts) of both connected and disconnected graphlets. In addition, an adaptive approach is introduced that finds the smallest sample size required to obtain estimates within a given user-defined error bound. On 300 networks from 20 domains, we obtain <1% relative error for all graphlets. This is significantly more accurate than existing methods while using less data. Moreover, it takes a few seconds on billion edge graphs (as opposed to days/weeks). These are by far the largest graphlet computations to date.

We study mechanisms to characterize how the asymptotic convergence of backpropagation in deep architectures, in general, is related to the network structure, and how it may be influenced by other design choices including activation type, denoising and dropout rate. We seek to analyze whether network architecture and input data statistics may guide the choices of learning parameters and vice versa. Given the broad applicability of deep architectures, this issue is interesting both from theoretical and a practical standpoint. Using properties of general nonconvex objectives (with first-order information), we first build the association between structural, distributional and learnability aspects of the network vis-\`a-vis their interaction with parameter convergence rates. We identify a nice relationship between feature denoising and dropout, and construct families of networks that achieve the same level of convergence. We then derive a workflow that provides systematic guidance regarding the choice of network sizes and learning parameters often mediated4 by input statistics. Our technical results are corroborated by an extensive set of evaluations, presented in this paper as well as independent empirical observations reported by other groups. We also perform experiments showing the practical implications of our framework for choosing the best fully-connected design for a given problem.