The current interpretation of stochastic gradient descent (SGD) as a stochastic process lacks generality in that its numerical scheme restricts continuous-time dynamics as well as the loss function and the distribution of gradient noise. We introduce a simplified scheme with milder conditions that flexibly interprets SGD as a discrete-time approximation of an Ito process. The scheme also works as a common foundation of SGD and stochastic gradient Langevin dynamics (SGLD), providing insights into their asymptotic properties. We investigate the convergence of SGD with biased gradient in terms of the equilibrium mode and the overestimation problem of the second moment of SGLD.

Analysis of somatic mutation profiles from cancer patients is essential in the development of cancer research. However, the low frequency of most mutations and the varying rates of mutations across patients makes the data extremely challenging to statistically analyze as well as difficult to use in classification problems, for clustering, visualization or for learning useful information. Thus, the creation of low dimensional representations of somatic mutation profiles that hold useful information about the DNA of cancer cells will facilitate the use of such data in applications that will progress precision medicine. In this paper, we talk about the open problem of learning from somatic mutations, and present Flatsomatic: a solution that utilizes variational autoencoders (VAEs) to create latent representations of somatic profiles. The work done in this paper shows great potential for this method, with the VAE embeddings performing better than PCA for a clustering task, and performing equally well to the raw high dimensional data for a classification task. We believe the methods presented herein can be of great value in future research and in bringing data-driven models into precision oncology.

Representing networks in a low dimensional latent space is a crucial task with many interesting applications in graph learning problems, such as link prediction and node classification. A widely applied network representation learning paradigm is based on the combination of random walks for sampling context nodes and the traditional Skip-Gram model to capture center-context node relationships. In this paper, we emphasize on exponential family distributions to capture rich interaction patterns between nodes in random walk sequences. We introduce the generic exponential family graph embedding model, that generalizes random walk-based network representation learning techniques to exponential family conditional distributions. We study three particular instances of this model, analyzing their properties and showing their relationship to existing unsupervised learning models. Our experimental evaluation on real-world datasets demonstrates that the proposed techniques outperform well-known baseline methods in two downstream machine learning tasks. Introduction Graphs or networks have become ubiquitous as data from diverse disciplines can naturally be represented as graph structures. Characteristics examples include social, collaboration, information and biological networks, or even networks that are generated by textual information. Besides, graphs are not only useful as models for data representation but can be proven valuable in prediction and learning tasks.

It is a particularly well-suited approach to better understand the underlying structure of data when scientific understanding of the data is at an early stage. BN modelling is designed to sort out directly from indirectly related variables and offers a far richer modelling framework than classical approaches in epidemiology like, e.g., regression techniques or extensions thereof. In contrast to structural equation modelling (Hair, Black, Babin, Anderson, Tatham et al. 1998), which requires expert knowledge to design the model, the Additive Bayesian Network (ABN) method is a data-driven approach (Lewis and Ward 2013; Kratzer, Pittavino, Lewis, and Furrer 2019b). It does not rely on expert knowledge, but it can possiarXiv:1911.09006v1

Determining the number of clusters present in a dataset is an important problem in cluster analysis. Conventional clustering techniques generally assume this parameter to be provided up front. In this paper, we propose a method which analyzes cluster stability for predicting the cluster number. Under the same computational framework, the technique also finds representatives of the clusters. The method is apt for handling big data, as we design the algorithm using Monte-Carlo simulation. Also, we explore a few pertinent issues found to be of also clustering. Experiments reveal that the proposed method is capable of identifying a single cluster. It is robust in handling high dimensional dataset and performs reasonably well over datasets having cluster imbalance. Moreover, it can indicate cluster hierarchy, if present. Overall we have observed significant improvement in speed and quality for predicting cluster numbers as well as the composition of clusters in a large dataset. Keywords: k-means clustering, Bipartite graph, Perfect Matching, Kuhn-Munkres Algorithm, Monte Carlo simulation. 1. Introduction In cluster analysis, it is required to group a set of data points in a multidimensional space, so that data points in the same group are more similar to each other than to those in other groups. These groups are called clusters. Various distance functions may be used to compute the degree of similarity or dissimilarity among these data points. Typically Euclidean distance function is widely used in clustering. The aim of this unsupervised technique is to increase homogeneity in a group and heterogeneity between groups. Several clustering methods with different characteristics have been proposed for different purposes. Some well-known methods include partition-based clustering [26], hierarchical clustering [25], spectral clustering [27], density-based clustering [12]. However, they require the knowledge of cluster number for a given dataset a priori [12, 21, 26, 27, 36].

As an adaptive, interpretable, robust, and accurate meta-algorithm for arbitrary differentiable loss functions, gradient tree boosting is one of the most popular machine learning techniques, though the computational expensiveness severely limits its usage. Stochastic gradient boosting could be adopted to accelerates gradient boosting by uniformly sampling training instances, but its estimator could introduce a high variance. This situation arises motivation for us to optimize gradient tree boosting. We combine gradient tree boosting with importance sampling, which achieves better performance by reducing the stochastic variance. Furthermore, we use a regularizer to improve the diagonal approximation in the Newton step of gradient boosting. The theoretical analysis supports that our strategies achieve a linear convergence rate on logistic loss. Empirical results show that our algorithm achieves a 2.5x--18x acceleration on two different gradient boosting algorithms (LogitBoost and LambdaMART) without appreciable performance loss.

When a black-box optimization objective can only be evaluated with costly or noisy measurements, most standard optimization algorithms are unsuited to find the optimal solution. Specialized algorithms that deal with exactly this situation make use of surrogate models. These models are usually continuous and smooth, which is beneficial for continuous optimization problems, but not necessarily for combinatorial problems. However, by choosing the basis functions of the surrogate model in a certain way, we show that it can be guaranteed that the optimal solution of the surrogate model is integer. This approach outperforms random search, simulated annealing and one Bayesian optimization algorithm on the problem of finding robust routes for a noise-perturbed traveling salesman benchmark problem, with similar performance as another Bayesian optimization algorithm, and outperforms all compared algorithms on a convex binary optimization problem with a large number of variables.

European satellite missions Sentinel-1 (S1) and Sentinel-2 (S2) provide at highspatial resolution and high revisit time, respectively, radar and optical imagesthat support a wide range of Earth surface monitoring tasks such as LandUse/Land Cover mapping. A long-standing challenge in the remote sensingcommunity is about how to efficiently exploit multiple sources of information and leverage their complementary. In this particular case, get the most out ofradar and optical satellite image time series (SITS). Here, we propose to dealwith land cover mapping through a deep learning framework especially tailoredto leverage the multi-source complementarity provided by radar and opticalSITS. The proposed architecture is based on an extension of Recurrent NeuralNetwork (RNN) enriched via a customized attention mechanism capable to fitthe specificity of SITS data. In addition, we propose a new pretraining strategythat exploits domain expert knowledge to guide the model parameter initial-ization. Thorough experimental evaluations involving several machine learningcompetitors, on two contrasted study sites, have demonstrated the suitabilityof our new attention mechanism combined with the extend RNN model as wellas the benefit/limit to inject domain expert knowledge in the neural networktraining process.

Uplift models support decision-making in marketing campaign planning. Estimating the causal effect of a marketing treatment, an uplift model facilitates targeting communication to responsive customers and efficient allocation of marketing budgets. Research into uplift models focuses on conversion models to maximize incremental sales. The paper introduces uplift modeling strategies for maximizing incremental revenues. If customers differ in their spending behavior, revenue maximization is a more plausible business objective compared to maximizing conversions. The proposed methodology entails a transformation of the prediction target, customer-level revenues, that facilitates implementing a causal uplift model using standard machine learning algorithms. The distribution of campaign revenues is typically zero-inflated because of many non-buyers. Remedies to this modeling challenge are incorporated in the proposed revenue uplift strategies in the form of two-stage models. Empirical experiments using real-world e-commerce data confirm the merits of the proposed revenue uplift strategy over relevant alternatives including uplift models for conver-sion and recently developed causal machine learning algorithms. To quantify the degree to which improved targeting decisions raise return on marketing, the paper develops a decomposition of campaign profit. Applying the decomposition to a digital coupon targeting campaign, the paper provides evidence that revenue uplift modeling, as well as causal machine learning, can improve cam-paign profit substantially.

The explosion of digital data has created multiple opportunities for organizations and individuals to leverage machine learning (ML) to transform the way they operate. However, the shortage of experts in the field of machine learning -- data scientists -- is often a setback to the use of ML. In an attempt to alleviate this shortage, multiple approaches for the automation of machine learning have been proposed in recent years. While these approaches are effective, they often require a great deal of time and computing resources. In this study, we propose RankML, a meta-learning based approach for predicting the performance of whole machine learning pipelines. Given a previously-unseen dataset, a performance metric, and a set of candidate pipelines, RankML immediately produces a ranked list of all pipelines based on their predicted performance. Extensive evaluation on 244 datasets, both in regression and classification tasks, shows that our approach either outperforms or is comparable to state-of-the-art, computationally heavy approaches while requiring a fraction of the time and computational cost.