The paper explores linear generalised complex structures over vector bundles.
problem Understanding holomorphic vector bundles in a generalized geometry context.
method Adapted linear splitting and equivalence to C-multiplication and C-Lie algebroid structure. result Generalised complex Lie algebroids are expressed as complex conjugated Lie bialgebroids.
New algorithm reduces regret in delayed feedback generalised linear bandits.
problem Regret in delayed feedback generalised linear bandits.
method Adaptation of optimistic algorithm to delayed feedback.
result Achieves a regret bound independent of the horizon's delay penalty.
Paper proves non-zero generalization boost for equivariant models.
problem Improving generalization in machine learning models.
method Analyzes simplest case of linear models, focusing on invariant/equivariant properties.
result First provably non-zero improvement in generalization for invariant/equivariant models.
Paper uses SLT to improve model selection for SHM.
problem Model selection for SHM using data-based systems.
method Utilizes Statistical Learning Theory to rigorously estimate generalisation.
result Incorporating domain knowledge improves model generalisation.
Study proposes new methods to convert betting odds into accurate probabilities for sports forecasting.
problem Convert betting odds to accurate outcome probabilities for sports forecasting and market efficiency analysis.
method Proposes two methods: Odds-Only-Equal-Profitability-Confidence (OO-EPC) and Favourite-Longshot-Bias-Adjusted Generalised Linear Model (FL-GLM).
result Proposed methods outperform existing methods in empirical tests and real-world applications.
This paper explains double descent in linear neural networks, identifying new factors.
problem Understanding double descent in linear neural networks.
method Gradient flow derivation and necessary conditions for double descent.
result Singular values of input-output covariance matrix are important for double descent in two-layer models.
We study generalised linear regression and classification for a synthetically generated dataset encompassing different problems of interest, such as learning with random features, neural networks in the lazy training regime, and the hidden manifold model. We consider the high-dimensional regime and using the replica me…
Study generalised Einstein metrics on Lie groups, classifying various types.
problem Classify left-invariant generalised Einstein metrics on Lie groups.
method New algebraic reformulation, classification based on Lie bracket and scalar product.
result Full classification of solvable and almost Abelian generalised Einstein Lie groups.
We present a general formalism for incorporating the string corrections in generalised geometry, which necessitates the extension of the generalised tangent bundle. Not only are such extensions obstructed, string symmetries and the existence of a well-defined effective action require a precise choice of the (generalise…
ARC algorithm optimizes dynamic pricing with correlated observations.
problem Optimizing dynamic pricing with correlated and generally distributed observations.
method Extends ARC algorithm to batched bandits with generalised linear model.
result ARC algorithm outperforms alternative approaches in dynamic pricing.
Proposes new methods for inference in GLMs without assuming model correctness.
problem Inference for GLMs assumes model correctness, leading to uncertainty and bias.
method Develops nonparametric estimands and uses influence curves with flexible procedures.
result Inference for GLM parameters is improved without model correctness assumptions.
New damping technique improves deep learning models by reducing noise in flat directions.
problem Improving generalization in deep learning models by reducing estimation noise in flat directions.
method Developed a novel random matrix theory based damping learner to reduce the shrinkage coefficient and improve generalization.
result Significant generalization improvements in logistic regression and deep neural networks experiments.
Stochastic linear bandits are a natural and simple generalisation of finite-armed bandits with numerous practical applications. Current approaches focus on generalising existing techniques for finite-armed bandits, notably the optimism principle and Thompson sampling. While prior work has mostly been in the worst-case …
The study characterizes learning Gaussian mixtures using GLMs in high dimensions.
problem Learning Gaussian mixtures with generalised linear models in high-dimensional settings.
method Empirical risk minimization with convex loss and regularisation.
result Exact asymptotics of the ERM estimator for Gaussian mixtures in high dimensions.
EVILL uses randomised perturbations to improve exploration in bandit problems.
problem Improving exploration in structured stochastic bandit problems.
method Solves for the minimiser of a linearly perturbed regularised negative log-likelihood function.
result EVILL matches the performance of Thompson-sampling-style methods in theory and practice.
We show that generalised geometry gives a unified description of maximally supersymmetric consistent truncations of ten- and eleven-dimensional supergravity. In all cases the reduction manifold admits a "generalised parallelisation" with a frame algebra with constant coefficients. The consistent truncation then arises …
Groups satisfy linear surface isoperimetric functions.
problem Isoperimetric functions for surface diagrams in hyperbolic groups.
method Analyzing word-hyperbolic groups and their surface diagrams.
result Linear isoperimetric functions for all surface types in hyperbolic groups.
In this article, we study a generalisation of the Seiberg-Witten equations, replacing the spinor representation with a hyperKahler manifold equipped with certain symmetries. Central to this is the construction of a (non-linear) Dirac operator acting on the sections of the non-linear fibre-bundle. For hyperKahler manifo…
Novel GLMMNet model tackles high-cardinality categorical features in actuarial applications.
problem Inadequate encoding methods for high-cardinality categorical features in actuarial data.
method Generalised Linear Mixed Model Neural Network (GLMMNet) integrating a generalised linear mixed model in a deep learning framework.
result GLMMNet often outperforms or performs comparably with entity embedded neural networks, providing transparency.
Recently Gay and Kirby described a new decomposition of smooth closed 4-manifolds called a trisection. This paper generalises Heegaard splittings of 3-manifolds and trisections of 4-manifolds to all dimensions, using triangulations as a key tool. In particular, we prove that every closed piecewise linear n-mani…
The paper analyzes fluctuations in ensemble models in high-dimensional settings.
problem Understanding statistical fluctuations in ensemble models in high-dimensional settings.
method Develops a rigorous theory for the study of fluctuations in ensemble of generalised linear models.
result Provides a complete description of the asymptotic joint distribution of the empirical risk minimizer for convex losses in high-dimensional settings.
Extends Calabi operator to Riemannian locally symmetric spaces.
problem Local integrability conditions on Riemannian locally symmetric spaces.
method Generalizes Calabi operator to Riemannian locally symmetric spaces.
result Generalised operator works in irreducible case and fails in products.
Proposes EM for sparse horseshoe estimation.
problem Sparse estimation of sparse parameter vectors using the horseshoe prior.
method Expectation-Maximisation (EM) procedure for MAP estimates.
result Our approach performs comparable or superior to state-of-the-art methods.
New method reveals why GNNs perform well on certain datasets.
problem Understanding why GNNs perform differently on similar datasets.
method Deriving exact generalization error for various GNN architectures.
result Benchmark datasets favor architectures that rely on graph structure.
Study shows bounds on volumes of weakly generalised alternating knots.
problem Volume bounds for weakly generalised alternating knots.
method Analysis of weakly generalised alternating knots in 3-manifolds.
result Upper volume bound does not hold for weakly generalised alternating knots.
The second fundamental form of Riemannian geometry is generalised to the case of a manifold with a linear connection and an integrable distribution. This bilinear form is generally not symmetric and its skew part is the torsion. The form itself is closely related to the shape map of the connection. The codimension one …
Maps of infectious disease---charting spatial variations in the force of infection, degree of endemicity, and the burden on human health---provide an essential evidence base to support planning towards global health targets. Contemporary disease mapping efforts have embraced statistical modelling approaches to properly…
Paper generalizes path signature using fractional calculus for improved machine learning.
problem Improving path signature for machine learning applications.
method Introduces two new signatures inspired by fractional calculus and machine learning considerations.
result Significant accuracy improvements in handwritten digit recognition.
This is a brief review of some of the uses of nonlinear sigma models. After a short general discussion touching on point particles, strings and condensed matter systems, focus is shifted to sigma models as probes of target space geometries. The relation of supersymmetric non-linear sigma models to Kähler, hyperkähler, …
The paper generalizes Cartan Geometry using Polacek and Siegel's approach.
problem Formulating sigma model dynamics in a covariant way.
method Using Polacek and Siegel's generalised curvature and torsion approach within the generalised metric formalism.
result Almost all higher generalised tensors correspond to covariant derivatives of the generalised Riemann tensor.
New bounds for shallow neural networks with deterministic parameters.
problem Developing generalisation bounds for shallow neural networks.
method PAC-Bayesian theory applied to shallow neural networks with deterministic parameters.
result Empirical non-vacuous bounds for shallow neural networks trained with vanilla SGD.
In a recent seminal paper \cite{D-H-R} of Dafermos, Holzegel and Rodnianski the linear stability of the Schwarzschild family of black hole solutions to the Einstein vacuum equations was established by imposing a double null gauge. In this paper we shall prove that the Schwarzschild family is linearly stable as solution…
Online DEM improves tracking of latent states in dynamic systems.
problem Tracking latent states in dynamic systems with online updates.
method Specializes DEM for online data assimilation, separating temporal scales.
result ODEM can track latent states of a non-linear generative model.
A generalised notion of connection on a fibre bundle E over a manifold M is presented. These connections are characterised by a smooth distribution on E which projects onto a (not necessarily integrable) distribution on M and which, in addition, is `parametrised' in some specific way by a vector bundle map from a presc…
Generative models converge to data distribution but not principal latent factors.
problem Understanding when generative models converge to the true data distribution.
method Analytical characterisation of transition from memorisation to generalisation in linear generative models.
result Convergence captures matching the bulk of the data distribution but not principal latent factors.
This paper presents a cross-country comparison of significant predictors of small business failure between Italy and the UK. Financial measures of profitability, leverage, coverage, liquidity, scale and non-financial information are explored, some commonalities and differences are highlighted. Several models are consid…
Two proofs of Kalman Theorem using flows of vector fields.
problem Classical result of Control Theory (Kalman Theorem).
method Two proofs using flows of vector fields.
result New criteria for local controllability of non-linear systems.
Study on dynamics of non-linear autoencoders learning principal components.
problem Technical difficulty in studying non-linear autoencoders due to non-trivial correlations.
method Derive asymptotically exact equations for SGD training of shallow, non-linear autoencoders.
result Autoencoders learn principal components sequentially and tie weights are ineffective.
New proof of generalized Chow-Rashevskii theorem for non-linear systems.
problem Generalized Chow-Rashevskii Theorem for non-linear systems.
method Independent proof structure allowing generalizations to orbits of compositions of flows.
result Proof structure applicable to applications in Control Theory and controllability criteria.
Introduces Exponentially Weighted Signature for better path representation.
problem Uniform treatment of historical information in signatures.
method Generalizes EFM signature to bounded linear operators, enabling contextualised temporal weighting.
result EWS is the unique solution to a linear controlled differential equation and generalizes state-space models.
We define (p,q) hermitian geometry as the target space geometry of the two dimensional (p,q) supersymmetric sigma model. This includes generalised Kähler geometry for (2,2), generalised hyperkähler geometry for (4,2), strong Kähler with torsion geometry for (2,1) and strong hyperkähler with torsion geometry f…
Develops a new GLM framework for claims reserving with adaptive estimation.
problem Accurate assessment of claims reserves with dynamic and dependent claim activity.
method Multivariate evolutionary GLM framework with adaptive particle filtering algorithm.
result Adaptive estimation of evolving factors improves claims reserve accuracy.
Classifies special quartic curves up to equivalence.
problem Classifying maximal quartic curves up to equivalence.
method Analyzing intersections of quartic polynomials and their level sets.
result Quartic generalised projective special real manifolds have non-regular boundary behavior.
This work uncovers algorithm-dependent regularisation in diffusion models.
problem Understanding and improving generalisation in high-dimensional diffusion models.
method Algorithmic stability and score stability analysis.
result Identifies multiple sources of implicit regularisation unique to diffusion models.
New PAC-Bayes bounds for unbounded loss functions.
problem Generalization bounds for learning problems with unbounded loss functions.
method Introducing HYPE, a new notion for loss range, and deriving a novel PAC-Bayesian generalization bound.
result PAC-Bayes framework extended to unbounded loss functions.
New methods combine model predictions to avoid linear mixtures' limitations.
problem Combining predictions from different models to avoid linear mixtures' limitations.
method Log-linear pooling (locking) and quantum superposition (quacking) to optimise model weights.
result Demonstrated locking method with illustrative example and practical application.
Graded bundles are a class of graded manifolds which represent a natural generalisation of vector bundles and include the higher order tangent bundles as canonical examples. We present and study the concept of the linearisation of graded bundle which allows us to define the notion of the linear dual of a graded bundle.…
Paper proposes GEG to enhance fairness in binary and multi-class classification.
problem Fairness in multi-class classification tasks is under-explored.
method Formulates multi-objective problem between effectiveness and fairness constraints, proposes GEG algorithm.
result GEG improves fairness up to 92% and decreases accuracy up to 14%.