Author name cluster

Aleksei Ustimenko

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8 papers

1 author row

ICML Conference 2024 Conference Paper

Deep Stochastic Mechanics

Elena Orlova
Aleksei Ustimenko
Ruoxi Jiang
Peter Y. Lu
Rebecca Willett

This paper introduces a novel deep-learning-based approach for numerical simulation of a time-evolving Schrödinger equation inspired by stochastic mechanics and generative diffusion models. Unlike existing approaches, which exhibit computational complexity that scales exponentially in the problem dimension, our method allows us to adapt to the latent low-dimensional structure of the wave function by sampling from the Markovian diffusion. Depending on the latent dimension, our method may have far lower computational complexity in higher dimensions. Moreover, we propose novel equations for stochastic quantum mechanics, resulting in quadratic computational complexity with respect to the number of dimensions. Numerical simulations verify our theoretical findings and show a significant advantage of our method compared to other deep-learning-based approaches used for quantum mechanics.

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ICLR Conference 2024 Conference Paper

Ito Diffusion Approximation of Universal Ito Chains for Sampling, Optimization and Boosting

Aleksei Ustimenko
Aleksandr Beznosikov

In this work, we consider rather general and broad class of Markov chains, Ito chains, that look like Euler-Maryama discretization of some Stochastic Differential Equation. The chain we study is a unified framework for theoretical analysis. It comes with almost arbitrary isotropic and state-dependent noise instead of normal and state-independent one as in most related papers. Moreover, in our chain the drift and diffusion coefficient can be inexact in order to cover wide range of applications as Stochastic Gradient Langevin Dynamics, sampling, Stochastic Gradient Descent or Stochastic Gradient Boosting. We prove the bound in $\mathcal{W}_{2}$-distance between the laws of our Ito chain and corresponding differential equation. These results improve or cover most of the known estimates. And for some particular cases, our analysis is the first.

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ICLR Conference 2023 Conference Paper

Gradient Boosting Performs Gaussian Process Inference

Aleksei Ustimenko
Artem Beliakov
Liudmila Prokhorenkova

This paper shows that gradient boosting based on symmetric decision trees can be equivalently reformulated as a kernel method that converges to the solution of a certain Kernel Ridge Regression problem. Thus, we obtain the convergence to a Gaussian Process' posterior mean, which, in turn, allows us to easily transform gradient boosting into a sampler from the posterior to provide better knowledge uncertainty estimates through Monte-Carlo estimation of the posterior variance. We show that the proposed sampler allows for better knowledge uncertainty estimates leading to improved out-of-domain detection.

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ICML Conference 2023 Conference Paper

Which Tricks are Important for Learning to Rank?

Ivan Lyzhin
Aleksei Ustimenko
Andrey Gulin
Liudmila Prokhorenkova

Nowadays, state-of-the-art learning-to-rank methods are based on gradient-boosted decision trees (GBDT). The most well-known algorithm is LambdaMART which was proposed more than a decade ago. Recently, several other GBDT-based ranking algorithms were proposed. In this paper, we thoroughly analyze these methods in a unified setup. In particular, we address the following questions. Is direct optimization of a smoothed ranking loss preferable over optimizing a convex surrogate? How to properly construct and smooth surrogate ranking losses? To address these questions, we compare LambdaMART with YetiRank and StochasticRank methods and their modifications. We also propose a simple improvement of the YetiRank approach that allows for optimizing specific ranking loss functions. As a result, we gain insights into learning-to-rank techniques and obtain a new state-of-the-art algorithm.

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ICML Conference 2021 Conference Paper

SGLB: Stochastic Gradient Langevin Boosting

Aleksei Ustimenko
Liudmila Prokhorenkova

This paper introduces Stochastic Gradient Langevin Boosting (SGLB) - a powerful and efficient machine learning framework that may deal with a wide range of loss functions and has provable generalization guarantees. The method is based on a special form of the Langevin diffusion equation specifically designed for gradient boosting. This allows us to theoretically guarantee the global convergence even for multimodal loss functions, while standard gradient boosting algorithms can guarantee only local optimum. We also empirically show that SGLB outperforms classic gradient boosting when applied to classification tasks with 0-1 loss function, which is known to be multimodal.

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ICLR Conference 2021 Conference Paper

Uncertainty in Gradient Boosting via Ensembles

Andrey Malinin
Liudmila Prokhorenkova
Aleksei Ustimenko

For many practical, high-risk applications, it is essential to quantify uncertainty in a model's predictions to avoid costly mistakes. While predictive uncertainty is widely studied for neural networks, the topic seems to be under-explored for models based on gradient boosting. However, gradient boosting often achieves state-of-the-art results on tabular data. This work examines a probabilistic ensemble-based framework for deriving uncertainty estimates in the predictions of gradient boosting classification and regression models. We conducted experiments on a range of synthetic and real datasets and investigated the applicability of ensemble approaches to gradient boosting models that are themselves ensembles of decision trees. Our analysis shows that ensembles of gradient boosting models successfully detect anomalous inputs while having limited ability to improve the predicted total uncertainty. Importantly, we also propose a concept of a virtual ensemble to get the benefits of an ensemble via only one gradient boosting model, which significantly reduces complexity.

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ICML Conference 2020 Conference Paper

StochasticRank: Global Optimization of Scale-Free Discrete Functions

Aleksei Ustimenko
Liudmila Prokhorenkova

In this paper, we introduce a powerful and efficient framework for direct optimization of ranking metrics. The problem is ill-posed due to the discrete structure of the loss, and to deal with that, we introduce two important techniques: stochastic smoothing and novel gradient estimate based on partial integration. We show that classic smoothing approaches may introduce bias and present a universal solution for a proper debiasing. Importantly, we can guarantee global convergence of our method by adopting a recently proposed Stochastic Gradient Langevin Boosting algorithm. Our algorithm is implemented as a part of the CatBoost gradient boosting library and outperforms the existing approaches on several learning-to-rank datasets. In addition to ranking metrics, our framework applies to any scale-free discrete loss function.

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ICML Conference 2019 Conference Paper

Learning to select for a predefined ranking

Aleksandr Vorobev
Aleksei Ustimenko
Gleb Gusev
Pavel Serdyukov

In this paper, we formulate a novel problem of learning to select a set of items maximizing the quality of their ordered list, where the order is predefined by some explicit rule. Unlike the classic information retrieval problem, in our setting, the predefined order of items in the list may not correspond to their quality in general. For example, this is a dominant scenario in personalized news and social media feeds, where items are ordered by publication time in a user interface. We propose new theoretically grounded algorithms based on direct optimization of the resulting list quality. Our offline and online experiments with a large-scale product search engine demonstrate the overwhelming advantage of our methods over the baselines in terms of all key quality metrics.

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