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Relations between average clustering coefficient and global clustering coefficient, local efficiency, radiality, closeness, betweenness and stress centralities were obtained for simple graphs.

Optimizing multiple objectives simultaneously is an important task for recommendation platforms to improve their performance. However, this task is particularly challenging since the relationships between different objectives are heterogeneous across different consumers and dynamically fluctuating according to different contexts. Especially in those cases when objectives become conflicting with each other, the result of recommendations will form a pareto-frontier, where the improvements of any objective comes at the cost of a performance decrease of another objective. Existing multi-objective recommender systems do not systematically consider such dynamic relationships; instead, they balance between these objectives in a static and uniform manner, resulting in only suboptimal multi-objective recommendation performance. In this paper, we propose a Deep Pareto Reinforcement Learning (DeepPRL) approach, where we (1) comprehensively model the complex relationships between multiple objectives in recommendations; (2) effectively capture personalized and contextual consumer preference for each objective to provide better recommendations; (3) optimize both the short-term and the long-term performance of multi-objective recommendations. As a result, our method achieves significant pareto-dominance over the state-of-the-art baselines in the offline experiments. Furthermore, we conducted a controlled experiment at the video streaming platform of Alibaba, where our method simultaneously improved three conflicting business objectives over the latest production system significantly, demonstrating its tangible economic impact in practice.

This book collects the lectures about graph theory and its applications which were given to students of mathematical departments of Moscow State University and Peking University. Graph theory is a very wide field with a lot of applications in almost every scientific area: in many branches of mathematics, computer science, physics, chemistry, biology and also in psychology, arts, philosophy and many others. Nowadays, graph theory becomes especially more important because of the rapid development of molecular biology, neural networks and AI fields. One of the aims of writing this book was to give students thorough knowledge about graphs to understand modern scientific fields more deeply. Here we tried to give classical and modern theorems and algorithms in more understandable and simple way. We spent many time to rewrite them and close the gaps in several simplest well-known proofs to provide more precise and accurate material for students.

Context has been an important topic in recommender systems over the past two decades. A standard representational approach to context assumes that contextual variables and their structures are known in an application. Most of the prior CARS papers following representational approach manually selected and considered only a few crucial contextual variables in an application, such as time, location, and company of a person. This prior work demonstrated significant recommendation performance improvements when various CARS-based methods have been deployed in numerous applications. However, some recommender systems applications deal with a much bigger and broader types of contexts, and manually identifying and capturing a few contextual variables is not sufficient in such cases. In this paper, we study such ``context-rich'' applications dealing with a large variety of different types of contexts. We demonstrate that supporting only a few most important contextual variables, although useful, is not sufficient. In our study, we focus on the application that recommends various banking products to commercial customers within the context of dialogues initiated by customer service representatives. In this application, we managed to identify over two hundred types of contextual variables. Sorting those variables by their importance forms the Long Tail of Context (LTC). In this paper, we empirically demonstrate that LTC matters and using all these contextual variables from the Long Tail leads to significant improvements in recommendation performance.

The purpose of this article is to demonstrate the connection between the properties of the Gromov--Hausdorff distance and the Borsuk conjecture. The Borsuk number of a given bounded metric space $X$ is the infimum of cardinal numbers $n$ such that $X$ can be partitioned into $n$ smaller parts (in the sense of diameter). An exact formula for the Gromov--Hausdorff distance between bounded metric spaces is obtained under the assumption that the diameter and cardinality of one space are less than the diameter and Borsuk number of another, respectively. Using the results of Bacon's equivalence between the Lusternik--Schnirelmann and Borsuk problems, several corollaries are obtained.

It is shown that any bounded metric space can be isometrically embedded into the Gromov--Hausdorff metric class GH. This result is a consequence of local geometry description of the class GH in a sufficiently small neighborhood of a generic metric space. This description is interesting in itself. The technique of optimal correspondences and their distortions is used., Comment: 15 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:2111.06709

The aim of this paper is to demonstrate relations between Gromov-Hausdorff distance properties and the Borsuk Conjecture. The Borsuk number of a given bounded metric space $X$ is the infimum of cardinal numbers $n$ such that $X$ can be partitioned into $n$ smaller parts (in the sense of diameter). An exact formula for the Gromov-Hausdorff distance between bounded metric spaces is obtained under the assumptions that the diameter and the cardinality of one space is less than the diameter and the Borsuk number of the other one, respectively. Using Bacon equivalence results between Lusternik-Schnirelmann and Borsuk Problems several corollaries are obtained., Comment: It is the same publication as arXiv:2203.04030. Sorry for inconveniences

We consider the proper class of all metric spaces endowed with the Gromov--Hausdorff distance. Its maximal subclasses, consisting of the spaces on finite distance from each other, we call clouds. Multiplying all distances in a metric space by the same positive real number, we obtain a similarity transformation of the Gromov--Hausdorff class. In our previous work, we observed that with such a transformation, some clouds can jump to others. To characterize the phenomenon, we studied the stabilizers of the similarity action. In this paper, we prove that every cloud with a nontrivial stabilizer has a center, i.e., a metric space for which all similarities from the stabilizer generate a new space at zero distance. Moreover, the center is unique modulo zero distance. The proof is based on the cloud completeness theorem., Comment: 17 pages

The paper is devoted to geometrical investigation of the Gromov-Hausdorff distance on the classes of all metric spaces and of all bounded metric spaces. The main attention is paid to pass connectivity questions. The pass connected components of the Gromov-Hausdorff class of all metric spaces are described, and the pass connectivity of spheres is proved in several particular cases., Comment: 16 pages

The paper is devoted to the study of the Gromov-Hausdorff proper class, consisting of all metric spaces considered up to isometry. In this class, a generalized Gromov-Hausdorff pseudometric is introduced and the geometry of the resulting space is investigated. The first main result is a proof of the completeness of the space, i.e., that all fundamental sequences converge in it. Then we partition the space into maximal proper subclasses consisting of spaces at a finite distance from each other. We call such subclasses clouds. A multiplicative similarity group operates on clouds, multiplying all the distances of each metric space by some positive number. We present examples of similarity mappings transferring some clouds into another ones. We also show that if a cloud contains a space that remains at zero distance from itself under action of all similarities, then such a cloud contracted to this space. In the final part, we investigate subsets of the real line with respect to their behavior under various similarities., Comment: 13 pages, 1 figure

We present an AutoML system called LightAutoML developed for a large European financial services company and its ecosystem satisfying the set of idiosyncratic requirements that this ecosystem has for AutoML solutions. Our framework was piloted and deployed in numerous applications and performed at the level of the experienced data scientists while building high-quality ML models significantly faster than these data scientists. We also compare the performance of our system with various general-purpose open source AutoML solutions and show that it performs better for most of the ecosystem and OpenML problems. We also present the lessons that we learned while developing the AutoML system and moving it into production.

Classical recommender system methods typically face the filter bubble problem when users only receive recommendations of their familiar items, making them bored and dissatisfied. To address the filter bubble problem, unexpected recommendations have been proposed to recommend items significantly deviating from user's prior expectations and thus surprising them by presenting "fresh" and previously unexplored items to the users. In this paper, we describe a novel Personalized Unexpected Recommender System (PURS) model that incorporates unexpectedness into the recommendation process by providing multi-cluster modeling of user interests in the latent space and personalized unexpectedness via the self-attention mechanism and via selection of an appropriate unexpected activation function. Extensive offline experiments on three real-world datasets illustrate that the proposed PURS model significantly outperforms the state-of-the-art baseline approaches in terms of both accuracy and unexpectedness measures. In addition, we conduct an online A/B test at a major video platform Alibaba-Youku, where our model achieves over 3\% increase in the average video view per user metric. The proposed model is in the process of being deployed by the company., Comment: Accepted to RecSys20

Cross domain recommender system constitutes a powerful method to tackle the cold-start and sparsity problem by aggregating and transferring user preferences across multiple category domains. Therefore, it has great potential to improve click-through-rate prediction performance in online commerce platforms having many domains of products. While several cross domain sequential recommendation models have been proposed to leverage information from a source domain to improve CTR predictions in a target domain, they did not take into account bidirectional latent relations of user preferences across source-target domain pairs. As such, they cannot provide enhanced cross-domain CTR predictions for both domains simultaneously. In this paper, we propose a novel approach to cross-domain sequential recommendations based on the dual learning mechanism that simultaneously transfers information between two related domains in an iterative manner until the learning process stabilizes. In particular, the proposed Dual Attentive Sequential Learning (DASL) model consists of two novel components Dual Embedding and Dual Attention, which jointly establish the two-stage learning process: we first construct dual latent embeddings that extract user preferences in both domains simultaneously, and subsequently provide cross-domain recommendations by matching the extracted latent embeddings with candidate items through dual-attention learning mechanism. We conduct extensive offline experiments on three real-world datasets to demonstrate the superiority of our proposed model, which significantly and consistently outperforms several state-of-the-art baselines across all experimental settings. We also conduct an online A/B test at a major video streaming platform Alibaba-Youku, where our proposed model significantly improves business performance over the latest production system in the company., Comment: Accepted to KDD21

Analysis of chest CT scans can be used in detecting parts of lungs that are affected by infectious diseases such as COVID-19.Determining the volume of lungs affected by lesions is essential for formulating treatment recommendations and prioritizingpatients by severity of the disease. In this paper we adopted an approach based on using an ensemble of deep convolutionalneural networks for segmentation of slices of lung CT scans. Using our models we are able to segment the lesions, evaluatepatients dynamics, estimate relative volume of lungs affected by lesions and evaluate the lung damage stage. Our modelswere trained on data from different medical centers. We compared predictions of our models with those of six experiencedradiologists and our segmentation model outperformed most of them. On the task of classification of disease severity, ourmodel outperformed all the radiologists.

Cross domain recommender systems have been increasingly valuable for helping consumers identify useful items in different applications. However, existing cross-domain models typically require large number of overlap users, which can be difficult to obtain in some applications. In addition, they did not consider the duality structure of cross-domain recommendation tasks, thus failing to take into account bidirectional latent relations between users and items and achieve optimal recommendation performance. To address these issues, in this paper we propose a novel cross-domain recommendation model based on dual learning that transfers information between two related domains in an iterative manner until the learning process stabilizes. We develop a novel latent orthogonal mapping to extract user preferences over multiple domains while preserving relations between users across different latent spaces. Furthermore, we combine the dual learning method with the metric learning approach, which allows us to significantly reduce the required common user overlap across the two domains and leads to even better cross-domain recommendation performance. We test the proposed model on two large-scale industrial datasets and six domain pairs, demonstrating that it consistently and significantly outperforms all the state-of-the-art baselines. We also show that the proposed model works well with very few overlap users to obtain satisfying recommendation performance comparable to the state-of-the-art baselines that use many overlap users., Comment: Accepted to IEEE TKDE. arXiv admin note: text overlap with arXiv:1910.05189

In this paper, we examine the effectiveness of various recommendation strategies in the mobile channel and their impact on consumers' utility and demand levels for individual products. We find significant differences in effectiveness among various recommendation strategies. Interestingly, recommendation strategies that directly embed social proofs for the recommended alternatives outperform other recommendations. Besides, recommendation strategies combining social proofs with higher levels of induced awareness due to the prescribed temporal diversity have an even stronger effect on the mobile channel. In addition, we examine the heterogeneity of the demand effect across items, users, and contextual settings, further verifying empirically the aforementioned information and persuasion mechanisms and generating rich insights. We also facilitate the estimation of causal effects in the presence of endogeneity using machine-learning methods. Specifically, we develop novel econometric instruments that capture product differentiation (isolation) based on deep-learning models of user-generated reviews. Our empirical findings extend the current knowledge regarding the heterogeneous impact of recommender systems, reconcile contradictory prior results in the related literature, and have significant business implications., Comment: Forthcoming at MIS Quarterly

We calculate the Gromov--Hausdorff distance between a line segment and a circle in the Euclidean plane. To do that, we introduced a few new notions like round spaces and nonlinearity degree of a metric space., Comment: 14 pages, 4 figures

The course was given at Peking University, Fall 2019. We discuss the following subjects: (1) Introduction to general topology, hyperspaces, metric and pseudometric spaces, graph theory. (2) Graphs in metric spaces, minimum spanning tree, Steiner minimal tree, Gromov minimal filling. (3) Hausdorff distance, Vietoris topology, Limits theory, inheritance of completeness, total boundedness, compactness by hyperspaces. (4) Gromov-Hausdorff distance, triangle inequality, positive definiteness for isometry classes of compact spaces, counterexample for boundedly compact spaces. (5) Gromov-Hausdorff distance for separable spaces in terms of their isometric images in \ell_\infty, correspondences, Gromov-Hausdorff distance in terms of correspondences. (6) Epsilon-isometries and Gromov-Hausdorff distance. (7) Irreducible correspondences and Gromov-Hausdorff distance. (8) Gromov-Hausdorff convergence, inheritance of metric and topological properties while Gromov-Hausdorff convergence. (9) Gromov-Hausdorff space (GH-space), optimal correspondences, existence of closed optimal correspondences for compact metric spaces, GH-space is geodesic. (10) Cover number, packing number, total boundedness, completeness, and separability of GH-space. (11) mst-spectrum in terms of GH-distances to simplexes, Steiner problem in GH-space. (12) GH-distance to simplexes with more points, GH-distance to simplexes with at most the same number of points. (13) Generalized Borsuk problem, solution of Generalized Borsuk problem in terms of GH-distances, clique covering number and chromatic number of simple graphs, their dualities, calculating these numbers in terms of GH-distances., Comment: 108 pages, 1 figure. The course was given at Peking University, Fall 2019

In this paper, first, we survey the concept of diffeological Fisher metric and its naturality, using functorial language of probability morphisms, and slightly extending L\^e's theory in \cite{Le2020} to include weakly $C^k$-diffeological statistical models. Then we introduce the resulting notions of the diffeological Fisher distance, the diffeological Hausdorff--Jeffrey measure and explain their role in classical and Bayesian nonparametric estimation problems in statistics., Comment: final version, 20 p.. version 1: 17 p. comments are welcome!

Holter monitoring, a long-term ECG recording (24-hours and more), contains a large amount of valuable diagnostic information about the patient. Its interpretation becomes a difficult and time-consuming task for the doctor who analyzes them because every heartbeat needs to be classified, thus requiring highly accurate methods for automatic interpretation. In this paper, we present a three-stage process for analysing Holter recordings with robustness to noisy signal. First stage is a segmentation neural network (NN) with encoderdecoder architecture which detects positions of heartbeats. Second stage is a classification NN which will classify heartbeats as wide or narrow. Third stage in gradient boosting decision trees (GBDT) on top of NN features that incorporates patient-wise features and further increases performance of our approach. As a part of this work we acquired 5095 Holter recordings of patients annotated by an experienced cardiologist. A committee of three cardiologists served as a ground truth annotators for the 291 examples in the test set. We show that the proposed method outperforms the selected baselines, including two commercial-grade software packages and some methods previously published in the literature., Comment: Accepted for publication on BIOSIGNALS 2021

In this paper geometry of Gromov-Hausdorff distance on the class of all metric spaces considered up to an isometry is investigated. For this class continuous curves and their lengths are defined, and it is shown that the Gromov-Hausdorff distance is intrinsic. Besides, metric segments are considered, i.e., the classes of points lying between two given ones, and an extension problem of such segments beyond their end-points is considered., Comment: 19 pages

We introduce a simple autoencoder based on hyperbolic geometry for solving standard collaborative filtering problem. In contrast to many modern deep learning techniques, we build our solution using only a single hidden layer. Remarkably, even with such a minimalistic approach, we not only outperform the Euclidean counterpart but also achieve a competitive performance with respect to the current state-of-the-art. We additionally explore the effects of space curvature on the quality of hyperbolic models and propose an efficient data-driven method for estimating its optimal value., Comment: Accepted at ACM RecSys 2020; 7 pages

Unexpected recommender system constitutes an important tool to tackle the problem of filter bubbles and user boredom, which aims at providing unexpected and satisfying recommendations to target users at the same time. Previous unexpected recommendation methods only focus on the straightforward relations between current recommendations and user expectations by modeling unexpectedness in the feature space, thus resulting in the loss of accuracy measures in order to improve unexpectedness performance. Contrast to these prior models, we propose to model unexpectedness in the latent space of user and item embeddings, which allows to capture hidden and complex relations between new recommendations and historic purchases. In addition, we develop a novel Latent Closure (LC) method to construct hybrid utility function and provide unexpected recommendations based on the proposed model. Extensive experiments on three real-world datasets illustrate superiority of our proposed approach over the state-of-the-art unexpected recommendation models, which leads to significant increase in unexpectedness measure without sacrificing any accuracy metric under all experimental settings in this paper., Comment: Accepted at ACM TIST

In this paper we study the problem of predicting clinical diagnoses from textual Electronic Health Records (EHR) data. We show the importance of this problem in medical community and present comprehensive historical review of the problem and proposed methods. As the main scientific contributions we present a modification of Bidirectional Encoder Representations from Transformers (BERT) model for sequence classification that implements a novel way of Fully-Connected (FC) layer composition and a BERT model pretrained only on domain data. To empirically validate our model, we use a large-scale Russian EHR dataset consisting of about 4 million unique patient visits. This is the largest such study for the Russian language and one of the largest globally. We performed a number of comparative experiments with other text representation models on the task of multiclass classification for 265 disease subset of ICD-10. The experiments demonstrate improved performance of our models compared to other baselines, including a fine-tuned Russian BERT (RuBERT) variant. We also show comparable performance of our model with a panel of experienced medical experts. This allows us to hope that implementation of this system will reduce misdiagnosis., Comment: To be published in the proceedings of 2020 International Conference on Artificial Intelligence in Medicine, Minneapolis MN, USA

Segmentation of ischemic stroke and intracranial hemorrhage on computed tomography is essential for investigation and treatment of stroke. In this paper, we modified the U-Net CNN architecture for the stroke identification problem using non-contrast CT. We applied the proposed DL model to historical patient data and also conducted clinical experiments involving ten experienced radiologists. Our model achieved strong results on historical data, and significantly outperformed seven radiologist out of ten, while being on par with the remaining three.

We address the problem of self-supervised learning on discrete event sequences generated by real-world users. Self-supervised learning incorporates complex information from the raw data in low-dimensional fixed-length vector representations that could be easily applied in various downstream machine learning tasks. In this paper, we propose a new method "CoLES", which adapts contrastive learning, previously used for audio and computer vision domains, to the discrete event sequences domain in a self-supervised setting. We deployed CoLES embeddings based on sequences of transactions at the large European financial services company. Usage of CoLES embeddings significantly improves the performance of the pre-existing models on downstream tasks and produces significant financial gains, measured in hundreds of millions of dollars yearly. We also evaluated CoLES on several public event sequences datasets and showed that CoLES representations consistently outperform other methods on different downstream tasks., Comment: SIGMOD'22

In this paper we present a novel approach to credit scoring of retail customers in the banking industry based on deep learning methods. We used RNNs on fine grained transnational data to compute credit scores for the loan applicants. We demonstrate that our approach significantly outperforms the baselines based on the customer data of a large European bank. We also conducted a pilot study on loan applicants of the bank, and the study produced significant financial gains for the organization. In addition, our method has several other advantages described in the paper that are very significant for the bank., Comment: KDD 2019

Cross domain recommender systems have been increasingly valuable for helping consumers identify the most satisfying items from different categories. However, previously proposed cross-domain models did not take into account bidirectional latent relations between users and items. In addition, they do not explicitly model information of user and item features, while utilizing only user ratings information for recommendations. To address these concerns, in this paper we propose a novel approach to cross-domain recommendations based on the mechanism of dual learning that transfers information between two related domains in an iterative manner until the learning process stabilizes. We develop a novel latent orthogonal mapping to extract user preferences over multiple domains while preserving relations between users across different latent spaces. Combining with autoencoder approach to extract the latent essence of feature information, we propose Deep Dual Transfer Cross Domain Recommendation (DDTCDR) model to provide recommendations in respective domains. We test the proposed method on a large dataset containing three domains of movies, book and music items and demonstrate that it consistently and significantly outperforms several state-of-the-art baselines and also classical transfer learning approaches., Comment: Accepted to WSDM 2020

In this paper, we propose a novel model RevGAN that automatically generates controllable and personalized user reviews based on the arbitrarily given sentimental and stylistic information. RevGAN utilizes the combination of three novel components, including self-attentive recursive autoencoders, conditional discriminators, and personalized decoders. We test its performance on the several real-world datasets, where our model significantly outperforms state-of-the-art generation models in terms of sentence quality, coherence, personalization and human evaluations. We also empirically show that the generated reviews could not be easily distinguished from the organically produced reviews and that they follow the same statistical linguistics laws., Comment: Accepted to EMNLP 2019

In the present paper we calculate the Gromov-Hausdorff distance between an arbitrary simplex (a metric space all whose non-zero distances are the same) and a finite metric space whose non-zero distances take two distinct values (so-called $2$-distance spaces). As a corollary, a complete solution to generalized Borsuk problem for the $2$-distance spaces is obtained. In addition, we derive formulas for the clique covering number and for the chromatic number of an arbitrary graph $G$ in terms of the Gromov-Hausdorff distance between a simplex and an appropriate $2$-distance space constructed by the graph $G$., Comment: 10 pages

In the present paper we investigate the Gromov--Hausdorff distances between a bounded metric space $X$ and so called simplex, i.e., a metric space all whose non-zero distances are the same. In the case when the simplex's cardinality does not exceed the cardinality of $X$, a new formula for this distance is obtained. The latter permits to derive an exact formula for the distance between a simplex and an ultrametric space., Comment: 10 pages

Multi-criteria recommender systems have been increasingly valuable for helping consumers identify the most relevant items based on different dimensions of user experiences. However, previously proposed multi-criteria models did not take into account latent embeddings generated from user reviews, which capture latent semantic relations between users and items. To address these concerns, we utilize variational autoencoders to map user reviews into latent embeddings, which are subsequently compressed into low-dimensional discrete vectors. The resulting compressed vectors constitute latent multi-criteria ratings that we use for the recommendation purposes via standard multi-criteria recommendation methods. We show that the proposed latent multi-criteria rating approach outperforms several baselines significantly and consistently across different datasets and performance evaluation measures., Comment: Accepted to RecSys19'

In the present paper the following Generalized Borsuk Problem is studied: Can a given bounded metric space $X$ be partitioned into a given number $m$ (probably an infinite one) of subsets, each of which has a smaller diameter than $X$? We give a complete answer to this question in terms of the Gromov-Hausdorff distance from $X$ to a simplex of cardinality $m$ and having a diameter less than $X$. Here a simplex is a metric space, all whose non-zero distances are the same.

Geometric characteristics of metric spaces that appear in formulas of the Gromov--Hausdorff distances from these spaces to so-called simplexes, i.e., to the metric spaces, all whose non-zero distances are the same are studied. The corresponding calculations essentially use geometry of partitions of these spaces. In the finite case, it gives the lengths of minimal spanning trees. A similar theory for compact metric spaces was worked out previously. In the present paper we generalize those results to any bounded metric space, and also, we simplify some proofs.

Providing unexpected recommendations is an important task for recommender systems. To do this, we need to start from the expectations of users and deviate from these expectations when recommending items. Previously proposed approaches model user expectations in the feature space, making them limited to the items that the user has visited or expected by the deduction of associated rules, without including the items that the user could also expect from the latent, complex and heterogeneous interactions between users, items and entities. In this paper, we define unexpectedness in the latent space rather than in the feature space and develop a novel Latent Convex Hull (LCH) method to provide unexpected recommendations. Extensive experiments on two real-world datasets demonstrate the effectiveness of the proposed model that significantly outperforms alternative state-of-the-art unexpected recommendation methods in terms of unexpectedness measures while achieving the same level of accuracy.

The present paper is devoted to studying of minimal parametric fillings of finite metric spaces (a version of optimal connection problem) by methods of Linear Programming. The estimate on the multiplicity of multi-tours appearing in the formula of weight of minimal fillings is improved, an alternative proof of this formula is obtained, and also explicit formulas for finite spaces consisting of $5$ and $6$ points are derived., Comment: 19 pages, 4 figures

We have constructed a realization of rectilinear geodesic (in the sense of~\cite{Memoli2018}), lying in Gromov-Hausdorff space, as a shortest geodesic w.r.t. the Hausdorff distance in an ambient metric space., Comment: 5 pages, 1 figure