Yury Maximov

The alternating current (AC) chance-constrained optimal power flow (CC-OPF) problem addresses the economic efficiency of electricity generation and delivery under generation uncertainty. The latter is intrinsic to modern power grids because of the high amount of renewables. Despite its academic success, the AC CC-OPF problem is highly nonlinear and computationally demanding, which limits its practical impact. For improving the AC-OPF problem complexity/accuracy trade-off, the paper proposes a fast data-driven setup that uses the sparse and hybrid Gaussian processes (GP) framework to model the power flow equations with input uncertainty. We advocate the efficiency of the proposed approach by a numerical study over multiple IEEE test cases that show up to two times speed-up and more accurate solutions over state-of-the-art methods.

Hail risk assessment is crucial for businesses, particularly in the agricultural and insurance sectors, as it helps estimate and mitigate potential losses. Although significant attention has been given to short-term hail forecasting, the lack of research on climatological-scale hail risk estimation adds to the overall complexity of this task. Hail events are rare and localized, making their prediction a long-term open challenge. One approach to address this challenge is to develop a model that classifies vertical profiles of meteorological variables as favorable for hail formation while neglecting important spatial and temporal information. The main advantages of this approach lie in its computational efficiency and scalability. A more advanced strategy involves combining convolutional layers and recurrent neural network blocks to process geospatial and temporal data, respectively. This study compares the effectiveness of these two approaches and introduces a model suitable for forecasting changes in hail frequency.

In this paper, we study the effect of non-stationarities and memory in the learnability of a sequential recommender system that exploits user's implicit feedback. We propose an algorithm, where model parameters are updated user per user by minimizing a ranking loss over blocks of items constituted by a sequence of unclicked items followed by a clicked one. We illustrate through empirical evaluations on four large-scale benchmarks that removing non-stationarities, through an empirical estimation of the memory properties, in user's behaviour interactions allows to gain in performance with respect to MAP and NDCG.

Having actual models for power system components, such as generators and loads or auxiliary equipment, is vital for a correct assessment of the power system operating state as well as establishing stability margins. Often, however, a power system operator has limited information about the actual values for power system components' parameters. Even if the model is available, its operating parameters, as well as the control settings, are time-dependent and subject to a real-time identification. Ideally, these parameters should be identified from measurement data, such as PMU signals. However, it is challenging to do this from the ambient measurements in the absence of transient dynamics since the signal to noise ratio (SNR) for such signals is not necessarily big. In this paper, we design a Bayesian framework for on-line identification of power system components' parameters based on ambient phasor measurement unit (PMU) data, that has reliable performance for SNR as low as five and for certain parameters can give good estimations even for unit SNR. Finally, we support the framework by a robust and time-efficient numerical method. We illustrate the approach efficiency on a synchronous generator example.

In this paper, we propose a theoretically founded sequential strategy for training large-scale Recommender Systems (RS) over implicit feedback mainly in the form of clicks. The proposed approach consists in minimizing pairwise ranking loss over blocks of consecutive items constituted by a sequence of non-clicked items followed by a clicked one for each user. Parameter updates are discarded if for a given user the number of sequential blocks is below or above some given thresholds estimated over the distribution of the number of blocks in the training set. This is to prevent from updating the parameters for an abnormally high number of clicks over some targeted items, mainly due to bots; or very few user interactions. Both scenarios affect the decision of RS and imply a shift over the distribution of items that are shown to the users. We provide a proof of convergence of the algorithm to the minimizer of the ranking loss, in the case where the latter is convex. Furthermore, experimental results on five large-scale collections demonstrate the efficiency of the proposed algorithm concerning the state-of-the-art approaches, both regarding different ranking measures and computation time.

Low-rank methods for semi-definite programming (SDP) have gained a lot of interest recently, especially in machine learning applications. Their analysis often involves determinant-based or Schatten-norm penalties, which are difficult to implement in practice due to high computational efforts. In this paper, we propose Entropy-Penalized Semi-Definite Programming (EP-SDP); which provides a unified framework for a broad class of penalty functions used in practice to promote a low-rank solution. We show that EP-SDP problems admit an efficient numerical algorithm, having (almost) linear time complexity of the gradient computation; this makes it useful for many machine learning and optimization problems. We illustrate the practical efficiency of our approach on several combinatorial optimization and machine learning problems.

We propose Rademacher complexity bounds for multi-class classifiers trained with a two-step semi-supervised model. In the first step, the algorithm partitions the partially labeled data and then identifies dense clusters containing kappa predominant classes using the labeled training examples such that the proportion of their non-predominant classes is below a fixed threshold stands for clustering consistency. In the second step, a classifier is trained by minimizing a margin empirical loss over the labeled training set and a penalization term measuring the disability of the learner to predict the i predominant classes of the identified clusters. The resulting data-dependent generalization error bound involves the margin distribution of the classifier, the stability of the clustering technique used in the first step and Rademacher complexity terms corresponding to partially labeled training data. Our theoretical result exhibit convergence rates extending those proposed in the literature for the binary case, and experimental results show empirical evidence that supports the theory.

Belief Propagation algorithms are instruments used broadly to solve graphical model optimization and statistical inference problems. In the general case of a loopy Graphical Model, Belief Propagation is a heuristic which is quite successful in practice, even though its empirical success, typically, lacks theoretical guarantees. This paper extends the short list of special cases where correctness and/or convergence of a Belief Propagation algorithm is proven. We generalize the formulation of MM-Sum Network Flow problem by relaxing the flow conservation (balance) constraints and then proving that the Belief Propagation algorithm converges to the exact result.

We propose a method for low-rank semidefinite programming in application to the semidefinite relaxation of unconstrained binary quadratic problems. The method improves an existing solution of the semidefinite programming relaxation to achieve a lower rank solution. This procedure is computationally efficient as it does not require projecting on the cone of positive-semidefinite matrices. Its performance in terms of objective improvement and rank reduction is tested over multiple graphs of large-scale Gset graph collection and over binary optimization problems from the Biq Mac collection.