We simplify Khovanov homology for torus braids using Gaussian elimination.
problem Computing Khovanov homology for torus braids is complex and computationally intensive.
method Applying Gaussian elimination to reduce the number of generators in the Khovanov chain complex.
result We provide a bound on the number of generators in the whittled complex at fixed homological degree.
NeurWIN learns Whittle indices for restless bandits using deep reinforcement learning.
problem Finding optimal solutions for restless bandits with complex transition kernels.
method NeurWIN uses a neural network to learn Whittle indices, leveraging the Whittle indices' mathematical properties.
result NeurWIN outperforms other RL algorithms in solving three recently studied restless bandit problems.
New algorithm uses Whittle index to improve Q-learning for restless bandits.
problem Optimizing decision-making in multiarmed restless bandits with average reward.
method Introduces a novel reinforcement learning algorithm combining Q-learning and Whittle index policy.
result Demonstrates significant computational gains and excellent empirical performance.
ContextWIN uses neural networks and reinforcement learning to optimize decisions in dynamic environments.
problem Optimizing decisions in dynamic, context-aware environments like recommendation systems.
method Integrates a mixture of experts within a reinforcement learning framework to compute context-specific weights for decision-making.
result Enhanced efficiency and accuracy in Whittle index computation for each arm in RMABs.
New algorithm optimizes resource allocation in non-stationary networks.
problem Optimal resource allocation in non-stationary RMABs is computationally hard.
method Sliding-Window Online Whittle (SW-Whittle) policy for non-stationary transition kernels.
result Sub-linear dynamic regret achieved with unknown variation budget.
Study Whittle index learning algorithms for restless bandits with constant stepsizes.
problem Optimizing decisions in restless multi-armed bandits with constant stepsizes.
method Developed Q-learning algorithms with constant stepsizes for index learning in restless bandits, extending to DQN and function approximations.
result The algorithms learn the Whittle index effectively.
Approximating Gaussian Whittle-Matern Fields over Well-Centered Triangulations of Riemannian Manifolds
problem Convergent approximation of Gaussian Whittle-Matern fields on Riemannian manifolds
method Finite Element approximation of SPDEs
result Universal approximation of precision and covariance matrices
Python package for estimating Hurst exponent in fBm.
problem Estimating Hurst exponent in fractional Brownian motion.
method Whittle's likelihood method applied to fractional Gaussian noise.
result Implementation achieves state-of-the-art accuracy and speed.
The Whittle likelihood is a widely used and computationally efficient pseudo-likelihood. However, it is known to produce biased parameter estimates for large classes of models. We propose a method for de-biasing Whittle estimates for second-order stationary stochastic processes. The de-biased Whittle likelihood can be …
We provide a computationally and statistically efficient method for estimating the parameters of a stochastic covariance model observed on a regular spatial grid in any number of dimensions. Our proposed method, which we call the Debiased Spatial Whittle likelihood, makes important corrections to the well-known Whittle…
Study on indexability of restless multi-armed bandits and rollout policy performance.
problem Maximizing discounted rewards in finite state restless multi-armed bandit problems.
method Decouple the problem into single-armed restless bandits, analyze using value iteration, and compare with Whittle index policy.
result Demonstrates conditions for indexability and compares performance of index policy and rollout policy.
New bandit model for healthcare intervention planning.
problem Maximizing patient health with limited monitoring resources.
method Developed Collapsing Bandits model and derived optimal policies.
result 3-order-of-magnitude speedup in algorithm performance.
Bayesian optimization on networks using Gaussian process models.
problem Optimizing expensive black-box functions on network structures.
method Developed Bayesian optimization algorithms with Gaussian process surrogates tailored to network geometry.
result Established regret bounds for smooth objective functions and analyzed practical cases.
This paper introduces the Markov-Switching Multifractal Duration (MSMD) model by adapting the MSM stochastic volatility model of Calvet and Fisher (2004) to the duration setting. Although the MSMD process is exponential β-mixing as we show in the paper, it is capable of generating highly persistent autocorrelation. W…
New ICA method for sources with mixed spectra.
problem Inaccurate separation of sources with temporal autocorrelations and mixed spectra.
method Estimates spectral density functions and line spectra using cubic splines and indicator functions, then maximizes the Whittle likelihood function.
result Outperforms existing ICA methods in simulations and EEG data applications.
There are three equivalent ways of representing two jointly observed real-valued signals: as a bivariate vector signal, as a single complex-valued signal, or as two analytic signals known as the rotary components. Each representation has unique advantages depending on the system of interest and the application goals. I…
Estimates network structure from correlated node outputs of wide-sense stationary processes.
problem Learning edge connectivity from node outputs of latent inputs.
method Wide-sense stationary stochastic processes, Laplacian matrix estimation, ℓ1-regularized Whittle's MLE.
result The MLE recovers the sparsity pattern of the Laplacian matrix with high probability.
We study the restless bandit associated with an extremely simple scalar Kalman filter model in discrete time. Under certain assumptions, we prove that the problem is indexable in the sense that the Whittle index is a non-decreasing function of the relevant belief state. In spite of the long history of this problem, thi…
Develops a measure-theoretic framework for complex co-occurrence data.
problem Modeling and interpreting complex co-occurrences in high-dimensional data.
method Introduces measure-theoretic probability and conditional probability, investigates E-integrals.
result Establishes a rigorous measure-theoretic foundation for co-occurrence modeling.
We introduce two new estimators of the bivariate Hurst exponent in the power-law cross-correlations setting -- the cross-periodogram and local X-Whittle estimators -- as generalizations of their univariate counterparts. As the spectrum-based estimators are dependent on a part of the spectrum taken into consideration …
cvHM framework speeds up GP inference for neural spike train analysis.
problem Scalability issue in approximate inference for latent GP models.
method cvHM framework using Hida-Matérn kernels and conjugate computation variational inference (CVI).
result Linear time inference for latent neural trajectories.
Restless bandit problems are instances of non-stationary multi-armed bandits. These problems have been studied well from the optimization perspective, where the goal is to efficiently find a near-optimal policy when system parameters are known. However, very few papers adopt a learning perspective, where the parameters…
We consider effort allocation in crowdsourcing, where we wish to assign labeling tasks to imperfect homogeneous crowd workers to maximize overall accuracy in a continuous-time Bayesian setting, subject to budget and time constraints. The Bayes-optimal policy for this problem is the solution to a partially observable Ma…
Study on rapid policy changes in reinforcement learning.
problem Rapid change of greedy policy in reinforcement learning.
method Empirical study and ablation analysis.
result Policy churn is a beneficial form of implicit exploration.
We examine the performance of six estimators of the power-law cross-correlations -- the detrended cross-correlation analysis, the detrending moving-average cross-correlation analysis, the height cross-correlation analysis, the averaged periodogram estimator, the cross-periodogram estimator and the local cross-Whittle e…
We study how the round-off (or discretization) error changes the statistical properties of a Gaussian long memory process. We show that the autocovariance and the spectral density of the discretized process are asymptotically rescaled by a factor smaller than one, and we compute exactly this scaling factor. Consequentl…
The paper tackles restless bandits with limited observation, proposing a method to analyze and approximate their optimal strategies.
problem Restless bandits with limited observation.
method General probabilistic model, PCL analysis, and approximation process.
result The proposed method can transform the problem into a finite-state problem, enabling the use of existing algorithms.
Abstract: Generalizes SGMs to infinite-dimensional Hilbertian setting.
problem Difficulties in extending SGMs to infinite-dimensional settings.
method Uses Gamma and Malliavin Calculus, Dirichlet forms, Wiener chaoses, and time-reversal formula.
result Generalized SGMs to Hilbertian setting with finite-dimensional entropic convergence bounds.
New approach tackles non-Markovian behavior in maternal health programs.
problem Improving adherence and engagement in maternal and child healthcare programs.
method Extending RMABs to non-Markovian settings, using time-series forecasting and TARI policy.
result Significant increase in engagement and content listened compared to existing methods.
The trade-off between the cost of acquiring and processing data, and uncertainty due to a lack of data is fundamental in machine learning. A basic instance of this trade-off is the problem of deciding when to make noisy and costly observations of a discrete-time Gaussian random walk, so as to minimise the posterior var…
Rough volatility models are continuous time stochastic volatility models where the volatility process is driven by a fractional Brownian motion with the Hurst parameter smaller than half, and have attracted much attention since a seminal paper titled "Volatility is rough" was posted on SSRN in 2014 showing that the log…
New model captures time series dependence across and within blocks.
problem Complex multivariate time series dependence structures.
method Time series Gaussian chain graph models with directed and undirected edges.
result Consistent recovery of time series chain graph structure.
The paper examines how long-memory dynamics, rough-volatility, and persistence affect equity volatility forecasting.
problem The study investigates how long-memory dynamics, rough-volatility, and persistence impact equity volatility forecasting.
method The paper combines semiparametric long-memory estimation, rough-volatility diagnostics, and structured forecasting regressions.
result Persistence measures improve out-of-sample volatility forecasts, particularly during periods of elevated market volatility and in volatility-managed portfolio applications.
New condition prevents hyperbolic spaces from matching curve complexes.
problem Identifying when hyperbolic spaces cannot match curve complexes.
method Analyzing specific hyperbolic complexes and identifying a condition.
result Identified a condition preventing quasi-isometry between hyperbolic spaces and curve complexes.
Study on complex line fields on almost-complex manifolds, proving existence conditions.
problem Existence of linearly independent complex line fields on almost-complex manifolds.
method Prove necessary and sufficient conditions for the existence of one, two, or three fields over certain manifolds.
result Necessary and sufficient condition for the existence of complex line fields over certain manifolds.
Homotopy types of curve and arc complexes are studied.
problem Understanding the homotopy types of curve and arc complexes.
method Proving homotopy equivalence and contractibility of complexes.
result Fine curve complex is homotopy equivalent to curve complex, fine arc complex is contractible.
This research explores complex-valued neural networks and their implementation.
problem The challenges of implementing complex-valued neural networks and their potential for non-complex data.
method Detailed theory and implementation of CVNN, including Wirtinger calculus, complex backpropagation, and modules like complex layers and activation functions. Python implementation using cvnn toolbox.
result Demonstrates the potential of CVNN for non-complex data through simulations.
Paper introduces fat CW complexes including all closed manifolds.
problem No specific problem stated, focuses on introducing new CW complexes.
method Introduces a new smooth version of CW complexes called fat CW complexes.
result Fat CW complexes include all closed manifolds and have desirable properties.
The paper discusses q-deformations of the Aomoto complex.
problem Deformation of cochain complexes associated with hyperplane arrangements.
method Replaces entries of coboundary maps with q-analogues and analyzes the resulting structures. result The q-deformation can be a cochain complex under certain conditions and yields local system cohomology groups. Study calculates global sections on complex curves.
problem Global sections of chiral de Rham complexes on complex curves.
method Calculation on closed complex curves with genus g ≥ 2.
result Space of global sections determined.
The paper studies lifts of complex structures on a manifold.
problem Understanding higher-order lifts of extended almost complex structures.
method Proved theorems on Nijenhuis tensor and introduced a new tensor field.
result Basic results on almost analytic complex vectors are investigated.
In this paper, we first provide an updated survey of the geometry of complex Cartan spaces. New characterizations for some particular classes of complex Cartan spaces are pointed out, e.g. Landsberg-Cartan, strongly Berwald-Cartan and others. We introduce the Cartan-Randers spaces which offer examples of Berwald-Cartan…
Study L2 Hilbert complexes on complex manifolds.
problem Analyse L2 Hilbert complexes on complex manifolds. method Define and study L2 Aeppli-Bott-Chern Hilbert complex; examine properties on various manifolds; use self-adjoint extensions of differential operators. result Kernels of operators on compact Hermitian manifolds are isomorphic to Aeppli or Bott-Chern cohomology.
The paper defines and constructs almost complex blow-ups on 4D almost complex manifolds.
problem Existence and uniqueness of almost complex blow-ups on almost complex manifolds.
method Definition and construction of almost complex blow-ups, proving their existence and uniqueness.
result Existence and uniqueness of almost complex blow-ups on 4D almost complex manifolds.
Research shows arc complex is not quasi-isometric to sphere complex.
problem Comparing quasi-isometry of arc complex and sphere complex.
method Simple proof of quasi-isometric rigidity of arc complex.
result Arc complex is not quasi-isometric to sphere complex.
Study Hodge-de Rham numbers for almost complex 4-manifolds, extending properties from complex surfaces.
problem Understanding Hodge-de Rham numbers for almost complex 4-manifolds.
method Introduced and studied Hodge-de Rham numbers, extending properties from complex surfaces.
result All Hodge-de Rham numbers for compact almost complex 4-manifolds are determined by the cohomology, except for one (the irregularity).
New proofs for growth series of Coxeter groups using complex structures.
problem Proving new formulae for growth series of Coxeter groups.
method Using the structure of Coxeter complexes, Davis complexes, or Tits non-complexes.
result Several classical formulae for growth series are proved in a new way.
In this article, we consider Cayley deformations of a compact complex surface in a Calabi--Yau four-fold. We will study complex deformations of compact complex submanifolds of Calabi--Yau manifolds with a view to explaining why complex and Cayley deformations of a compact complex surface are the same. We in fact prove …