arXiv subjects

Alexander Y. Shestopaloff

Publications and source records attributed to Alexander Y. Shestopaloff.

At least 19 recordsLinked to original sources

arXiv2025

Bayesian Markov-Switching Partial Reduced-Rank Regression

Reduced-Rank (RR) regression is a powerful dimensionality reduction technique but it overlooks any possible group configuration among the responses by assuming a low-rank structure on the entire coefficient matrix. Moreover, the temporal change of the relations between predictors and responses in time series induce a possibly time-varying grouping structure in the responses. To address these limitations, a Bayesian Markov-switching partial RR (MS-PRR) model is proposed, where the response vector is partitioned in two groups to reflect different complexity of the relationship. A \textit{simple} group assumes a low-rank linear regression, while a \textit{complex} group exploits nonparametric regression via a Gaussian Process. Differently from traditional approaches, group assignments and rank are treated as unknown parameters to be estimated. Then temporal persistence in the regression function is accounted for by a Markov-switching process that drives the changes in the grouping structure and model parameters over time. Full Bayesian inference is preformed via a partially collapsed Gibbs sampler, which allows uncertainty quantification without the need for trans-dimensional moves. Applications to two real-world macroeconomic and commodity data demonstrate the evidence of time-varying grouping and different degrees of complexity both across states and within each state.

stat.ME↗

arXiv2025

The Market Maker's Dilemma: Navigating the Fill Probability vs. Post-Fill Returns Trade-Off

Using data from a live trading experiment on the Binance Bitcoin perpetual, we examine the effects of (i) basic order book mechanics and (ii) the persistence of price changes from immediate to short timescales, revealing the interplay between returns, queue sizes, and orders' queue positions. We document a fundamental trade-off: a negative correlation between maker fill likelihood and post-fill returns. This dictates that viable maker strategies often require a contrarian approach, counter-trading the prevailing order book imbalance. These dynamics render commonly-cited strategies highly unprofitable, leading us to model `Reversals': situations where a contrarian maker strategy at the touch proves effective.

q-fin.TR↗

arXiv2025

MINERVA: Mutual Information Neural Estimation for Supervised Feature Selection

Existing feature filters rely on statistical pair-wise dependence metrics to model feature-target relationships, but this approach may fail when the target depends on higher-order feature interactions rather than individual contributions. We introduce Mutual Information Neural Estimation Regularized Vetting Algorithm (MINERVA), a novel approach to supervised feature selection based on neural estimation of mutual information between features and targets. We paramaterize the approximation of mutual information with neural networks and perform feature selection using a carefully designed loss function augmented with sparsity-inducing regularizers. Our method is implemented in a two-stage process to decouple representation learning from feature selection, ensuring better generalization and a more accurate expression of feature importance. We present examples of ubiquitous dependency structures that are rarely captured in literature and show that our proposed method effectively captures these complex feature-target relationships by evaluating feature subsets as an ensemble. Experimental results on synthetic and real-life fraud datasets demonstrate the efficacy of our method and its ability to perform exact solutions.

cs.LG↗

arXiv2025

A clusterability test for directed graphs

In this article, we extend a statistical test of graph clusterability, the $δ$ test, to directed graphs with no self loops. The $δ$ test, originally designed for undirected graphs, is based on the premise that graphs with a clustered structure display a mean local density that is statistically higher than the graph's global density. We posit that graphs that do not meet this necessary (but not sufficient) condition for clusterability can be considered unsuited to clustering. In such cases, vertex clusters do not offer a meaningful summary of the broader graph. Additionally in this study, we aim to determine the optimal sample size (number of neighborhoods). Our test, designed for the analysis of large networks, is based on sampling subsets of neighborhoods/nodes. It is designed for cases where computing the density of every node's neighborhood is infeasible. Our results show that the $δ$ test performs very well, even with very small samples of neighborhoods ($1\%$). It accurately detects unclusterable graphs and is also shown to be robust to departures from the underlying assumptions of the $t$ test.

cs.NI↗

arXiv2025

ClusterLOB: Enhancing Trading Strategies by Clustering Orders in Limit Order Books

In the rapidly evolving world of financial markets, understanding the dynamics of limit order book (LOB) is crucial for unraveling market microstructure and participant behavior. We introduce ClusterLOB as a method to cluster individual market events in a stream of market-by-order (MBO) data into different groups. To do so, each market event is augmented with six time-dependent features. By applying the K-means++ clustering algorithm to the resulting order features, we are then able to assign each new order to one of three distinct clusters, which we identify as directional, opportunistic, and market-making participants, each capturing unique trading behaviors. Our experimental results are performed on one year of MBO data containing small-tick, medium-tick, and large-tick stocks from NASDAQ. To validate the usefulness of our clustering, we compute order flow imbalances across each cluster within 30-minute buckets during the trading day. We treat each cluster's imbalance as a signal that provides insights into trading strategies and participants' responses to varying market conditions. To assess the effectiveness of these signals, we identify the trading strategy with the highest Sharpe ratio in the training dataset, and demonstrate that its performance in the test dataset is superior to benchmark trading strategies that do not incorporate clustering. We also evaluate trading strategies based on order flow imbalance decompositions across different market event types, including add, cancel, and trade events, to assess their robustness in various market conditions. This work establishes a robust framework for clustering market participant behavior, which helps us to better understand market microstructure, and inform the development of more effective predictive trading signals with practical applications in algorithmic trading and quantitative finance.

q-fin.TR↗

arXiv2025

Generalized Factor Neural Network Model for High-dimensional Regression

We tackle the challenges of modeling high-dimensional data sets, particularly those with latent low-dimensional structures hidden within complex, non-linear, and noisy relationships. Our approach enables a seamless integration of concepts from non-parametric regression, factor models, and neural networks for high-dimensional regression. Our approach introduces PCA and Soft PCA layers, which can be embedded at any stage of a neural network architecture, allowing the model to alternate between factor modeling and non-linear transformations. This flexibility makes our method especially effective for processing hierarchical compositional data. We explore ours and other techniques for imposing low-rank structures on neural networks and examine how architectural design impacts model performance. The effectiveness of our method is demonstrated through simulation studies, as well as applications to forecasting future price movements of equity ETF indices and nowcasting with macroeconomic data.

stat.ML↗

arXiv2025

A unifying framework for generalised Bayesian online learning in non-stationary environments

We propose a unifying framework for methods that perform probabilistic online learning in non-stationary environments. We call the framework BONE, which stands for generalised (B)ayesian (O)nline learning in (N)on-stationary (E)nvironments. BONE provides a common structure to tackle a variety of problems, including online continual learning, prequential forecasting, and contextual bandits. The framework requires specifying three modelling choices: (i) a model for measurements (e.g., a neural network), (ii) an auxiliary process to model non-stationarity (e.g., the time since the last changepoint), and (iii) a conditional prior over model parameters (e.g., a multivariate Gaussian). The framework also requires two algorithmic choices, which we use to carry out approximate inference under this framework: (i) an algorithm to estimate beliefs (posterior distribution) about the model parameters given the auxiliary variable, and (ii) an algorithm to estimate beliefs about the auxiliary variable. We show how the modularity of our framework allows for many existing methods to be reinterpreted as instances of BONE, and it allows us to propose new methods. We compare experimentally existing methods with our proposed new method on several datasets, providing insights into the situations that make each method more suitable for a specific task. We provide a Jax open source library to facilitate the adoption of this framework.

stat.ML↗

arXiv2024

Bayesian Partial Reduced-Rank Regression

Reduced-rank (RR) regression may be interpreted as a dimensionality reduction technique able to reveal complex relationships among the data parsimoniously. However, RR regression models typically overlook any potential group structure among the responses by assuming a low-rank structure on the coefficient matrix. To address this limitation, a Bayesian Partial RR (BPRR) regression is exploited, where the response vector and the coefficient matrix are partitioned into low- and full-rank sub-groups. As opposed to the literature, which assumes known group structure and rank, a novel strategy is introduced that treats them as unknown parameters to be estimated. The main contribution is two-fold: an approach to infer the low- and full-rank group memberships from the data is proposed, and then, conditionally on this allocation, the corresponding (reduced) rank is estimated. Both steps are carried out in a Bayesian approach, allowing for full uncertainty quantification and based on a partially collapsed Gibbs sampler. It relies on a Laplace approximation of the marginal likelihood and the Metropolized Shotgun Stochastic Search to estimate the group allocation efficiently. Applications to synthetic and real-world data reveal the potential of the proposed method to reveal hidden structures in the data.

stat.ME↗

arXiv2024

Outlier-robust Kalman Filtering through Generalised Bayes

We derive a novel, provably robust, and closed-form Bayesian update rule for online filtering in state-space models in the presence of outliers and misspecified measurement models. Our method combines generalised Bayesian inference with filtering methods such as the extended and ensemble Kalman filter. We use the former to show robustness and the latter to ensure computational efficiency in the case of nonlinear models. Our method matches or outperforms other robust filtering methods (such as those based on variational Bayes) at a much lower computational cost. We show this empirically on a range of filtering problems with outlier measurements, such as object tracking, state estimation in high-dimensional chaotic systems, and online learning of neural networks.

stat.ML↗

arXiv2024

Uncertainty Quantification in Bayesian Reduced-Rank Sparse Regressions

Reduced-rank regression recognises the possibility of a rank-deficient matrix of coefficients. We propose a novel Bayesian model for estimating the rank of the coefficient matrix, which obviates the need for post-processing steps and allows for uncertainty quantification. Our method employs a mixture prior on the regression coefficient matrix along with a global-local shrinkage prior on its low-rank decomposition. Then, we rely on the Signal Adaptive Variable Selector to perform sparsification and define two novel tools: the Posterior Inclusion Probability uncertainty index and the Relevance Index. The validity of the method is assessed in a simulation study, and then its advantages and usefulness are shown in real-data applications on the chemical composition of tobacco and on the photometry of galaxies.

stat.ME↗

arXiv2023

Robust Detection of Lead-Lag Relationships in Lagged Multi-Factor Models

In multivariate time series systems, key insights can be obtained by discovering lead-lag relationships inherent in the data, which refer to the dependence between two time series shifted in time relative to one another, and which can be leveraged for the purposes of control, forecasting or clustering. We develop a clustering-driven methodology for robust detection of lead-lag relationships in lagged multi-factor models. Within our framework, the envisioned pipeline takes as input a set of time series, and creates an enlarged universe of extracted subsequence time series from each input time series, via a sliding window approach. This is then followed by an application of various clustering techniques, (such as k-means++ and spectral clustering), employing a variety of pairwise similarity measures, including nonlinear ones. Once the clusters have been extracted, lead-lag estimates across clusters are robustly aggregated to enhance the identification of the consistent relationships in the original universe. We establish connections to the multireference alignment problem for both the homogeneous and heterogeneous settings. Since multivariate time series are ubiquitous in a wide range of domains, we demonstrate that our method is not only able to robustly detect lead-lag relationships in financial markets, but can also yield insightful results when applied to an environmental data set.

stat.ML↗

arXiv2023

Dynamic Time Warping for Lead-Lag Relationships in Lagged Multi-Factor Models

In multivariate time series systems, lead-lag relationships reveal dependencies between time series when they are shifted in time relative to each other. Uncovering such relationships is valuable in downstream tasks, such as control, forecasting, and clustering. By understanding the temporal dependencies between different time series, one can better comprehend the complex interactions and patterns within the system. We develop a cluster-driven methodology based on dynamic time warping for robust detection of lead-lag relationships in lagged multi-factor models. We establish connections to the multireference alignment problem for both the homogeneous and heterogeneous settings. Since multivariate time series are ubiquitous in a wide range of domains, we demonstrate that our algorithm is able to robustly detect lead-lag relationships in financial markets, which can be subsequently leveraged in trading strategies with significant economic benefits.

q-fin.ST↗

arXiv2022

Statistical network isomorphism

Graph isomorphism is a problem for which there is no known polynomial-time solution. Nevertheless, assessing (dis)similarity between two or more networks is a key task in many areas, such as image recognition, biology, chemistry, computer and social networks. Moreover, questions of similarity are typically more general and their answers more widely applicable than the more restrictive isomorphism question. In this article, we offer a statistical answer to the following questions: a) {\it ``Are networks $G_1$ and $G_2$ similar?''}, b) {\it ``How different are the networks $G_1$ and $G_2$?''} and c) {\it ``Is $G_3$ more similar to $G_1$ or $G_2$?''}. Our comparisons begin with the transformation of each graph into an all-pairs distance matrix. Our node-node distance, Jaccard distance, has been shown to offer a good reflection of the graph's connectivity structure. We then model these distances as probability distributions. Finally, we use well-established statistical tools to gauge the (dis)similarities in terms of probability distribution (dis)similarity. This comparison procedure aims to detect (dis)similarities in connectivity structure, not in easily observable graph characteristics, such as degrees, edge counts or density. We validate our hypothesis that graphs can be meaningfully summarized and compared via their node-node distance distributions, using several synthetic and real-world graphs. Empirical results demonstrate its validity and the accuracy of our comparison technique.

stat.CO↗

arXiv2021

Fragmentation, Price Formation, and Cross-Impact in Bitcoin Markets

In light of micro-scale inefficiencies induced by the high degree of fragmentation of the Bitcoin trading landscape, we utilize a granular data set comprised of orderbook and trades data from the most liquid Bitcoin markets, in order to understand the price formation process at sub-1 second time scales. To achieve this goal, we construct a set of features that encapsulate relevant microstructural information over short lookback windows. These features are subsequently leveraged first to generate a leader-lagger network that quantifies how markets impact one another, and then to train linear models capable of explaining between 10% and 37% of total variation in $500$ms future returns (depending on which market is the prediction target). The results are then compared with those of various PnL calculations that take trading realities, such as transaction costs, into account. The PnL calculations are based on natural $\textit{taker}$ strategies (meaning they employ market orders) that we associate to each model. Our findings emphasize the role of a market's fee regime in determining its propensity to being a leader or a lagger, as well as the profitability of our taker strategy. Taking our analysis further, we also derive a natural $\textit{maker}$ strategy (i.e., one that uses only passive limit orders), which, due to the difficulties associated with backtesting maker strategies, we test in a real-world live trading experiment, in which we turned over 1.5 million USD in notional volume. Lending additional confidence to our models, and by extension to the features they are based on, the results indicate a significant improvement over a naive benchmark strategy, which we also deploy in a live trading environment with real capital, for the sake of comparison.

q-fin.TR↗

arXiv2020

Graph Distances and Clustering

With a view on graph clustering, we present a definition of vertex-to-vertex distance which is based on shared connectivity. We argue that vertices sharing more connections are closer to each other than vertices sharing fewer connections. Our thesis is centered on the widely accepted notion that strong clusters are formed by high levels of induced subgraph density, where subgraphs represent clusters. We argue these clusters are formed by grouping vertices deemed to be similar in their connectivity. At the cluster level (induced subgraph level), our thesis translates into low mean intra-cluster distances. Our definition differs from the usual shortest-path geodesic distance. In this article, we compare three distance measures from the literature. Our benchmark is the accuracy of each measure's reflection of intra-cluster density, when aggregated (averaged) at the cluster level. We conduct our tests on synthetic graphs generated using the planted partition model, where clusters and intra-cluster density are known in advance. We examine correlations between mean intra-cluster distances and intra-cluster densities. Our numerical experiments show that Jaccard and Otsuka-Ochiai offer very accurate measures of density, when averaged over vertex pairs within clusters.

cs.DM↗

arXiv2020

A Statistical Density-Based Analysis of Graph Clustering Algorithm Performance

Measuring graph clustering quality remains an open problem. To address it, we introduce quality measures based on comparisons of intra- and inter-cluster densities, an accompanying statistical test of the significance of their differences and a step-by-step routine for clustering quality assessment. Our null hypothesis does not rely on any generative model for the graph, unlike modularity which uses the configuration model as a null model. Our measures are shown to meet the axioms of a good clustering quality function, unlike the very commonly used modularity measure. They also have an intuitive graph-theoretic interpretation, a formal statistical interpretation and can be easily tested for significance. Our work is centered on the idea that well clustered graphs will display a significantly larger intra-cluster density than inter-cluster density. We develop tests to validate the existence of such a cluster structure. We empirically explore the behavior of our measures under a number of stress test scenarios and compare their behavior to the commonly used modularity and conductance measures. Empirical stress test results confirm that our measures compare very favorably to the established ones. In particular, they are shown to be more responsive to graph structure and less sensitive to sample size and breakdowns during numerical implementation and less sensitive to uncertainty in connectivity. These features are especially important in the context of larger data sets or when the data may contain errors in the connectivity patterns.

cs.SI↗

arXiv2019

Replica Conditional Sequential Monte Carlo

We propose a Markov chain Monte Carlo (MCMC) scheme to perform state inference in non-linear non-Gaussian state-space models. Current state-of-the-art methods to address this problem rely on particle MCMC techniques and its variants, such as the iterated conditional Sequential Monte Carlo (cSMC) scheme, which uses a Sequential Monte Carlo (SMC) type proposal within MCMC. A deficiency of standard SMC proposals is that they only use observations up to time $t$ to propose states at time $t$ when an entire observation sequence is available. More sophisticated SMC based on lookahead techniques could be used but they can be difficult to put in practice. We propose here replica cSMC where we build SMC proposals for one replica using information from the entire observation sequence by conditioning on the states of the other replicas. This approach is easily parallelizable and we demonstrate its excellent empirical performance when compared to the standard iterated cSMC scheme at fixed computational complexity.

stat.CO↗

arXiv2017

New reconstruction and data processing methods for regression and interpolation analysis of multidimensional big data

The problems of computational data processing involving regression, interpolation, reconstruction and imputation for multidimensional big datasets are becoming more important these days, because of the availability of data and their widely spread usage in business, technological, scientific and other applications. The existing methods often have limitations, which either do not allow, or make it difficult to accomplish many data processing tasks. The problems usually relate to algorithm accuracy, applicability, performance (computational and algorithmic), demands for computational resources, both in terms of power and memory, and difficulty working with high dimensions. Here, we propose a new concept and introduce two methods, which use local area predictors (input data) for finding outcomes. One method uses the gradient based approach, while the second one employs an introduced family of smooth approximating functions. The new methods are free from many drawbacks of existing approaches. They are practical, have very wide range of applicability, provide high accuracy, excellent computational performance, fit for parallel computing, and very well suited for processing high dimension big data. The methods also provide multidimensional outcome, when needed. We present numerical examples of up to one hundred dimensions, and report in detail performance characteristics and various properties of new methods.

stat.ME↗