Study on geometry of Dirichlet distributions using Fisher-Rao metric.
problem Understanding the geometry of Dirichlet distributions.
method Analysis of Fisher-Rao metric on Dirichlet distribution parameter space.
result Geodesic completeness and negative sectional curvature of the space.
The asymptotic concentration of the Fr{é}chet mean of IID random variables on a Rieman-nian manifold was established with a central limit theorem by Bhattacharya \& Patrangenaru (BP-CLT) [6]. This asymptotic result shows that the Fr{é}chet mean behaves almost as the usual Euclidean case for sufficiently concentrated di…
The paper introduces new geometric methods to analyze radar electromagnetic wave statistics.
problem Analyzing spatio-temporal and polarimetric fluctuations of radar electromagnetic waves.
method Using statistical mechanics and Information Geometry, the paper defines a Fréchet barycentre and maximum entropy density for radar measurements.
result New tools for describing radar electromagnetic wave fluctuations, including a distance on covariance matrices.
In [16], a new family of vector-valued risk measures called multivariate expectiles is introduced. In this paper, we focus on the asymptotic behavior of these measures in a multivariate regular variations context. For models with equivalent tails, we propose an estimator of these multivariate asymptotic expectiles, in …
New formulas for geodesics on Stiefel and flag manifolds using trust-region method.
problem Computing geodesics and logarithms on Stiefel and flag manifolds.
method Closed-form geodesic formulas, trust-region solver, Fréchet derivatives.
result Efficient computation of geodesic distance and logarithm map.
New metrics defined for full-rank correlation matrices, ensuring unique operations.
problem No suitable problem statement as the abstract does not describe a problem to be solved.
method New Riemannian metrics defined on full-rank correlation matrices, providing unique operations.
result Unique Riemannian logarithm and Fréchet mean defined for full-rank correlation matrices.
We study geodesics of the form γ(t)=π(exp(tX)exp(tY)), $X,Y\in \fr{g}=\operatorname{Lie}(G)$, in homogeneous spaces G/K, where π:G→G/K is the natural projection. These curves naturally generalise homogeneous geodesics, that is orbits of one-parameter subgroups of G (i.e. γ(t)=π(exp(tX)), $X\in …
Constructs supermartingale couplings with full marginals constraints.
problem Optimal transport for supermartingale couplings with multiple marginals.
method Markovian iteration of one-period optimal supermartingale couplings.
result Explicit construction of supermartingale processes solving optimal transport problem.
We study geodesics in generalized Wallach spaces which are expressed as orbits of products of three exponential terms. These are homogeneous spaces M=G/K whose isotropy representation decomposes into a direct sum of three submodules m=m1⊕m2⊕m3, satisfying the relations $[\fr…
FGBoost boosts gradient boosting for complex data.
problem Gradient boosting struggles with non-Euclidean data.
method Introduces FGBoost for geodesic metric spaces.
result FGBoost performs well on complex data.
Let G be a compact connected simple Lie group and let $M=G^{\bb{C}}/P=G/K$ be a generalized flag manifold. In this article we focus on an important invariant of G/K, the so called $\fr{t}$-root system $R_{\fr{t}}$, and we introduce the notion of symmetric $\fr{t}$-triples, that is triples of $\fr{t}$-roots $ξ, ζ, η…
Study uses ML to analyze how interest rates affect fund returns, finding gradient boosting is effective.
problem Understanding how interest rate changes impact fund returns.
method Combines Machine Learning and causal inference, using Double Machine Learning framework.
result Gradient boosting is useful for predicting fund returns, showing a significant negative effect of interest rate increases.
We consider in this paper the FRS-deformations of a family of space curves with codimension ≤3. Some geometric aspects of a space curve such as flattenings, vertices and twistings points has been studied.
A new method for estimating large-scale linear models with improved precision.
problem Estimating large-scale linear statistical models efficiently.
method Sequential Least-Squares Estimators with Fast Randomized Sketching (SLSE-FRS), integrating Sketch-and-Solve and Iterative-Sketching methods.
result SLSE-FRS produces high-precision estimators, outperforming state-of-the-art methods.
Study shows splitting schemes can approximate WFR flows faster than the exact flow.
problem Improving sampling efficiency in Wasserstein-Fisher-Rao gradient flows.
method Investigates operator splitting techniques to numerically approximate WFR flows.
result A judicious choice of step size and operator ordering can lead to faster convergence of split schemes to the target distribution.
Phishing as one of the most well-known cybercrime activities is a deception of online users to steal their personal or confidential information by impersonating a legitimate website. Several machine learning-based strategies have been proposed to detect phishing websites. These techniques are dependent on the features …
FR-Train improves fair and robust AI training by detecting and reducing poisoned data.
problem Training AI models that are fair and robust in the presence of data bias and poisoning.
method Mutual information-based adversarial training with an additional discriminator.
result FR-Train maintains fairness and accuracy even in the presence of poisoned data.
Proves FR-NGD optimally approximates evolutionary dynamics and continuous Bayesian inference.
problem Optimizing continuous time replicator equations and continuous Bayesian inference.
method Fisher-Rao natural gradient descent (FR-NGD) and its correspondence with evolutionary dynamics.
result FR-NGD optimally approximates continuous time replicator equations and continuous Bayesian inference.
FR-LUX optimizes portfolio management by learning cost-aware policies robust to market conditions.
problem Transaction costs and regime shifts cause failure in live trading portfolios.
method Integrates three ingredients: microstructure-consistent execution model, trade-space trust region, and explicit regime conditioning.
result Achieves top average Sharpe ratio, maintains flat cost-performance slope, and superior risk-return efficiency.
Consider an anchored bundle (E,ρ), i.e. a vector bundle E→M equipped with a bundle map ρ:E→TM covering the identity. M.~Kapranov showed in the context of Lie-Rinehard algebras that there exists an extension of this anchored bundle to an infinite rank universal free Lie algebroid FR(E)⊃E. We …
Introduces a new geometric framework for field theories.
problem Developing a rigorous mathematical framework for field theories.
method Introduces supergeometric homotopy theory to physics.
result Classical bosonic field theories fit naturally into smooth sets.
We recall an extension of Kirby's Calculus on non-simply connected 3-manifolds given in [FR], and the surgery calculus of bridged links from [Ke], which involves only local moves. We give a short combinatorial proof that the two calculi are equivalent, and thus describe the same classes of 3-manifolds. This makes the p…
This study provides an explicit expansion of KL divergence's gradient flow in Fisher-Rao geometry.
problem Sampling techniques struggle to traverse between modes in non-convex potential functions.
method Explicit expansion of KL divergence's gradient flow in Fisher-Rao geometry.
result The convergence rate to π is independent of the potential function.
This article follow the article {http://hal.archives-ouvertes.fr/hal-00361030/fr/} in which the author characterize the fact of being of finite volume for a convex projective surface. We show here that the moduli space βf(Σg,p) of the convex projective structure on the surface Σg,p of genius g with p pun…
A new category generates 1D tangle invariants.
problem Developing a new category for 1D tangles.
method Proving a new (∞,1)-category has universal mapping property. result The new category generates link invariants.
New method improves fairness of facial recognition systems.
problem Facial recognition systems exhibit bias across different demographic groups.
method Optimizes centroid-based scores to reduce bias in pre-trained models.
result Demonstrates significant improvement in fairness with minimal loss in accuracy.
GeoIB uses information geometry to control compression in deep learning models.
problem The indirect and biased nature of traditional IB implementations in deep learning.
method GeoIB uses Fisher-Rao and Jacobian-Frobenius terms to control information compression directly.
result GeoIB achieves better trade-off between accuracy and compression than traditional IB methods.
This paper introduces a new Urban Point Cloud Dataset for Automatic Segmentation and Classification acquired by Mobile Laser Scanning (MLS). We describe how the dataset is obtained from acquisition to post-processing and labeling. This dataset can be used to learn classification algorithm, however, given that a great a…
We introduce \texttt{pycobra}, a Python library devoted to ensemble learning (regression and classification) and visualisation. Its main assets are the implementation of several ensemble learning algorithms, a flexible and generic interface to compare and blend any existing machine learning algorithm available in Pytho…
Study reveals centralization in Bitcoin transactions involving retail users.
problem Centralization and bias in Bitcoin transaction data.
method Heuristic classification of Bitcoin users, weekly activity pattern analysis.
result Most real transactions involve Frequent Receivers, centralizing the ecosystem.
Many tasks in modern machine learning can be formulated as finding equilibria in \emph{sequential} games. In particular, two-player zero-sum sequential games, also known as minimax optimization, have received growing interest. It is tempting to apply gradient descent to solve minimax optimization given its popularity a…
We construct examples of finitely generated groups L that have non-trivial actions on R-trees but which cannot act, without fixing a vertex, on any simplicial tree. Moreover, any finitely presented group mapping onto L does have a fixed point-free action on some simplicial tree.
Improved action recognition in live videos with hybrid FR-DL method.
problem High computational costs and lack of temporal information in conventional action recognition.
method Automated selection of representative frames, feature extraction, background subtraction, HOG, deep neural network, LSTM, Softmax-KNN classifier.
result Significant improvement in accuracy and speed compared to state-of-the-art methods.
Unified framework for discrete diffusion modeling with flexible noising processes.
problem Efficient modeling of large discrete state spaces with arbitrary corruption dynamics.
method Generalized Discrete Diffusion from Snapshots (GDDS) framework that supports uniformization for fast noising and snapshot-based ELBO for reverse process.
result GDDS outperforms existing discrete diffusion methods in training efficiency and generation quality.
Motivation: Prediction of ligands for proteins of known 3D structure is important to understand structure-function relationship, predict molecular function, or design new drugs. Results: We explore a new approach for ligand prediction in which binding pockets are represented by atom clouds. Each target pocket is compar…
New algorithm for multi-armed bandits with delayed, partially observed rewards.
problem Sequential decision-making with delayed feedback.
method Proposed multi-armed bandits with generalized temporally-partitioned rewards, introducing β-spread property.
result Upper bound on performance of TP-UCB-FR-G algorithm improves state of the art.
New method restores source features for SFDA without source data.
problem Domain adaptation without access to source data.
method Feature Restoration (FR) and Bottom-Up Feature Restoration (BUFR).
result BUFR outperforms existing SFDA methods in accuracy, calibration, and data efficiency.
New algorithms improve sampling from complex distributions.
problem Sampling from complex probability distributions efficiently.
method Regime-switching Langevin dynamics and Monte Carlo algorithms.
result Convergence guarantees and iteration complexities provided.
New method to calculate 3-manifold invariants via skew-racks.
problem Calculating invariants of 3-manifolds.
method Introducing skew-racks with good involution and Property FR, defining cocycle invariants.
result Established new approach to obtain 3-manifold invariants via Dehn surgery.
Sprays on Frechet manifolds connect connections and tangent structures.
problem Characterizing linear symmetric connections on Frechet manifolds.
method Constructing connection maps and linear symmetric connections on tangent and second-order tangent bundles using sprays.
result A bijective correspondence exists between linear symmetric connections on tangent bundles and sprays.
The performance of the state-of-the-art image segmentation methods heavily relies on the high-quality annotations, which are not easily affordable, particularly for medical data. To alleviate this limitation, in this study, we propose a weakly supervised image segmentation method based on a deep geodesic prior. We hypo…
In this paper, a direct continuation of math.DG/0411165, we generalize S. Lie's linearization criterion of an ordinary second order differential equation to the case of several independent variables (x^1, x^2 ..., x^n), n >1, and a single dependent variable y. Strikingly, as in math.DG/0411165, the (complicated) charac…
A new method for analyzing shapes and forms using additive models on manifolds.
problem Analyzing shapes and forms under geometric transformations.
method Extending generalized additive regression to models for shapes/forms using squared geodesic distance and Riemannian L2-Boosting algorithm. result Automated model selection and intuitive visualization of covariate effects in shape/form space.
Fair MP-Boost improves fairness and interpretability in boosting methods.
problem Improving fairness and interpretability in boosting methods.
method Fair MP-Boost uses adaptive sampling of minipatches to balance accuracy and fairness.
result Fair MP-Boost enhances fairness and accuracy while providing interpretable feature importance.
The smoothing theory is revised to generalize to different disc embedding spaces.
problem Generalizing the smoothing theory to various disc embedding spaces.
method Revising the Morlet-Burghelea-Lashof-Kirby-Siebenmann theorem to apply to different versions of disc smooth embedding spaces.
result The delooping of disc embedding spaces is shown to be compatible with the Hatcher and Budney actions.
MP-Boost boosts accuracy faster and more interpretable than AdaBoost.
problem Developing a faster, more interpretable boosting method.
method Adaptive selection of minipatches (small subsets of instances and features) at each iteration.
result Achieves comparable accuracy to AdaBoost and gradient boosting but faster and more interpretable.
Delta hedging, which plays a crucial rôle in modern financial engineering, is a tracking control design for a "risk-free" management. We utilize the existence of trends in financial time series (Fliess M., Join C.: A mathematical proof of the existence of trends in financial time series, Proc. Int. Conf. Systems Theory…
Boost-R uses gradient boosted trees for analyzing recurrence data.
problem Analyzing recurrence data with static and dynamic features.
method Gradient boosted additive trees with time-dependent functions.
result Estimates the cumulative intensity function of recurrent event processes.