arXiv subjects

André Fujita

Publications and source records attributed to André Fujita.

8 recordsLinked to original sources

arXiv2026

Directed Q-Analysis and Directed Higher-Order Connectivity on Digraphs: A Quantitative Approach

Traditional graph analysis focuses on nodes and edges, that is, pairwise relationships. Yet many real-world networks, including biological, social, and communication networks, involve higher-order relationships in which multiple nodes interact simultaneously. This has led many to develop network topology analysis methods based on higher-order structures and higher-order connectivity, seeking to reveal complex interactions beyond node pairs. Many of the latter address only undirected networks. To overcome this, we lay out a mathematical formalism resting on directed clique complexes constructed from directed graphs (their "higher-order structures" or "simplicial structures''), stressing the interrelations between directed cliques (their "directed higher-order connectivities''), leading towards a more complete directed Q-analysis that allows quantifying, characterizing, and comparing similarities involving simplicial structures.

math.GM↗

arXiv2026

Macro-aware time series forecasting via hierarchical mixed-frequency attention models

Deep learning models show promise in financial forecasting, yet their generalization is often undermined by small datasets, noisy signals, and non-stationarity. While meta-learning and related techniques mitigate some of these issues, they typically do not account for a core limitation in macro-financial prediction: the scarcity of distinct macroeconomic regimes that drive asset returns. We introduce HANET (Hierarchical Attention Network), a hybrid LSTM-based architecture that integrates macroeconomic domain knowledge through attention over long-run macro contexts while preserving high-frequency market dynamics. HANET organizes information in a hierarchical mixed-frequency structure, with daily asset-return signals nested within monthly macroeconomic windows, and introduces a Hierarchical Cross-Attention mechanism that reconciles low-frequency macro signals with high-frequency returns without discarding granular daily information. By framing regime selection as attention over macroeconomic contexts, the model adapts to scarce and shifting regimes. Empirically, across 55 liquid futures spanning multiple asset classes, HANET consistently outperforms neural forecasters that ignore macroeconomic information, particularly during turbulent periods, improving risk-adjusted returns and mitigating losses. Ablation studies show that these gains rely on structured macro conditioning rather than naive feature augmentation: an LSTM with the same macro representation performs poorly, and shuffling macro contexts substantially degrades performance. Finally, HANET provides interpretability through attention weights, highlighting which historical regimes are most influential for each forecast and linking macro conditions to portfolio outcomes. These results establish HANET as a systematic approach to integrating macroeconomic information into attention-based deep learning for financial forecasting.

q-fin.ST↗

arXiv2025

Tactical Asset Allocation with Macroeconomic Regime Detection

This paper extends the tactical asset allocation literature by incorporating regime modeling using techniques from machine learning. We propose a novel model that classifies current regimes, forecasts the distribution of future regimes, and integrates these forecasts with the historical performance of individual assets to optimize portfolio allocations. Utilizing a macroeconomic data set from the FRED-MD database, our approach employs a modified k-means algorithm to ensure consistent regime classification over time. We then leverage these regime predictions to estimate expected returns and volatilities, which are subsequently mapped into portfolio allocations using various sizing schemes. Our method outperforms traditional benchmarks such as equal-weight, buy-and-hold, and random regime models. Additionally, we are the first to apply a regime detection model from a large macroeconomic dataset to tactical asset allocation, demonstrating significant improvements in portfolio performance. Our work presents several key contributions, including a novel data-driven regime detection algorithm tailored for uncertainty in forecasted regimes and applying the FRED-MD data set for tactical asset allocation.

q-fin.PM↗

arXiv2021

Spectral density of random graphs: convergence properties and application in model fitting

Random graph models are used to describe the complex structure of real-world networks in diverse fields of knowledge. Studying their behavior and fitting properties are still critical challenges, that in general, require model specific techniques. An important line of research is to develop generic methods able to fit and select the best model among a collection. Approaches based on spectral density (i.e., distribution of the graph adjacency matrix eigenvalues) are appealing for that purpose: they apply to different random graph models. Also, they can benefit from the theoretical background of random matrix theory. This work investigates the convergence properties of model fitting procedures based on the graph spectral density and the corresponding cumulative distribution function. We also review results on the convergence of the spectral density for the most widely used random graph models. Moreover, we explore through simulations the limits of these graph spectral density convergence results, particularly in the case of the block model, where only partial results have been established.

math.ST↗

arXiv2020

Stage I non-small cell lung cancer stratification by using a model-based clustering algorithm with covariates

Lung cancer is currently the leading cause of cancer deaths. Among various subtypes, the number of patients diagnosed with stage I non-small cell lung cancer (NSCLC), particularly adenocarcinoma, has been increasing. It is estimated that 30 - 40\% of stage I patients will relapse, and 10 - 30\% will die due to recurrence, clearly suggesting the presence of a subgroup that could be benefited by additional therapy. We hypothesize that current attempts to identify stage I NSCLC subgroup failed due to covariate effects, such as the age at diagnosis and differentiation, which may be masking the results. In this context, to stratify stage I NSCLC, we propose CEM-Co, a model-based clustering algorithm that removes/minimizes the effects of undesirable covariates during the clustering process. We applied CEM-Co on a gene expression data set composed of 129 subjects diagnosed with stage I NSCLC and successfully identified a subgroup with a significantly different phenotype (poor prognosis), while standard clustering algorithms failed.

stat.AP↗

arXiv2015

Correlation between graphs with an application to brain networks analysis

The global functional brain network (graph) is more suitable for characterizing brain states than local analysis of the connectivity of brain regions. Therefore, graph-theoretic approaches are the natural methods to study the brain. However, conventional graph theoretical analyses are limited due to the lack of formal statistical methods for estimation and inference for random graphs. For example, the concept of correlation between two vectors of graphs is yet not defined. The aim of this article to introduce a notion of correlation between graphs. In order to develop a framework to infer correlation between graphs, we assume that they are generated by mathematical models and that the parameters of the models are our random variables. Then, we define that two vectors of graphs are independent whether their parameters are independent. The problem is that, in real world, the model is rarely known, and consequently, the parameters cannot be estimated. By analyzing the graph spectrum, we showed that the spectral radius is highly associated with the parameters of the graph model. Based on it, we constructed a framework for correlation inference between graphs and illustrate our approach in a functional magnetic resonance imaging data composed of 814 subjects comprising 529 controls and 285 individuals diagnosed with autism spectrum disorder (ASD). Results show that correlations between default-mode and control, default-mode and somatomotor, and default-mode and visual sub-networks are higher ($p<0.05$) in ASD than in controls.

stat.ME↗

arXiv2013

A statistical test to identify differences in clustering structures

Statistical inference on functional magnetic resonance imaging (fMRI) data is an important task in brain imaging. One major hypothesis is that the presence or not of a psychiatric disorder can be explained by the differential clustering of neurons in the brain. In view of this fact, it is clearly of interest to address the question of whether the properties of the clusters have changed between groups of patients and controls. The normal method of approaching group differences in brain imaging is to carry out a voxel-wise univariate analysis for a difference between the mean group responses using an appropriate test (e.g. a t-test) and to assemble the resulting "significantly different voxels" into clusters, testing again at cluster level. In this approach of course, the primary voxel-level test is blind to any cluster structure. Direct assessments of differences between groups (or reproducibility within groups) at the cluster level have been rare in brain imaging. For this reason, we introduce a novel statistical test called ANOCVA - ANalysis Of Cluster structure Variability, which statistically tests whether two or more populations are equally clustered using specific features. The proposed method allows us to compare the clustering structure of multiple groups simultaneously, and also to identify features that contribute to the differential clustering. We illustrate the performance of ANOCVA through simulations and an application to an fMRI data set composed of children with ADHD and controls. Results show that there are several differences in the brain's clustering structure between them, corroborating the hypothesis in the literature. Furthermore, we identified some brain regions previously not described, generating new hypothesis to be tested empirically.

stat.ME↗

arXiv2012

Discriminating different classes of biological networks by analyzing the graphs spectra distribution

The brain's structural and functional systems, protein-protein interaction, and gene networks are examples of biological systems that share some features of complex networks, such as highly connected nodes, modularity, and small-world topology. Recent studies indicate that some pathologies present topological network alterations relative to norms seen in the general population. Therefore, methods to discriminate the processes that generate the different classes of networks (e.g., normal and disease) might be crucial for the diagnosis, prognosis, and treatment of the disease. It is known that several topological properties of a network (graph) can be described by the distribution of the spectrum of its adjacency matrix. Moreover, large networks generated by the same random process have the same spectrum distribution, allowing us to use it as a "fingerprint". Based on this relationship, we introduce and propose the entropy of a graph spectrum to measure the "uncertainty" of a random graph and the Kullback-Leibler and Jensen-Shannon divergences between graph spectra to compare networks. We also introduce general methods for model selection and network model parameter estimation, as well as a statistical procedure to test the nullity of divergence between two classes of complex networks. Finally, we demonstrate the usefulness of the proposed methods by applying them on (1) protein-protein interaction networks of different species and (2) on networks derived from children diagnosed with Attention Deficit Hyperactivity Disorder (ADHD) and typically developing children. We conclude that scale-free networks best describe all the protein-protein interactions. Also, we show that our proposed measures succeeded in the identification of topological changes in the network while other commonly used measures (number of edges, clustering coefficient, average path length) failed.

stat.ME↗