Develops a test for strict stationarity in stochastic processes.
problem Testing strict stationarity of discrete time stochastic processes.
method Window averaged sample estimate of second order cumulant spectrum, asymptotic complex standard normal distribution test.
result Test statistic derived and demonstrated with 137Cs gamma ray decay data.
The paper explores cost-aware spectrum access strategies in cognitive radio systems.
problem Optimizing spectrum usage in cognitive radio systems with uncertain channel states and costs.
method Discrete time model with sensing and transmission phases, considering random costs and rewards.
result The optimal policy for spectrum access has a recursive double threshold structure, and online algorithms achieve near-optimal performance.
Study resource allocation strategies in sequential decisions with unknown rewards.
problem Sequential resource allocation with unknown rewards.
method Design combinatorial multi-armed bandit algorithms for discrete or continuous budgets.
result Prove algorithms achieve logarithmic cumulative regret under semi-bandit feedback.
We analyze the cumulative distribution of total personal income of USA counties, and gross domestic product of Brazilian, German and United Kingdom counties, and also of world countries. We verify that generalized exponential distributions, related to nonextensive statistical mechanics, describe almost the whole spectr…
Study of correlated Wigner matrices with BBP transitions.
problem Understanding spectral transitions in correlated Wigner matrices.
method Analyzes a Wigner-type matrix with row/column correlations, decomposes into bulk and outliers, and uses integral operators to model transitions.
result Correlated Wigner matrices exhibit multiple BBP transitions at critical points.
Study quantifies how LLMs capture higher-order statistical structure using cumulant expansion.
problem Understanding how LLMs internalize statistical structure during next-token prediction.
method Cumulant-expansion framework treating softmax entropy as perturbation around center distribution.
result Cumulants reveal distinct signatures for mathematical vs. general text prompts, quantifying feature-learning dynamics.
The CSA-ES is an Evolution Strategy with Cumulative Step size Adaptation, where the step size is adapted measuring the length of a so-called cumulative path. The cumulative path is a combination of the previous steps realized by the algorithm, where the importance of each step decreases with time. This article studies …
Using methods introduced by Scargle in 1978 we derive a cumulative version of the Lomb periodogram that exhibits frequency independent statistics when applied to cumulative noise. We show how this cumulative Lomb periodogram allows us to estimate the significance of log-periodic signatures in the S&P 500 anti-bubble th…
Kernelized cumulants improve statistical analysis in high-dimensional spaces.
problem Statistical analysis in high-dimensional spaces with low variance estimators.
method Extending cumulants to RKHS using tensor algebra and kernel trick.
result Kernelized cumulants provide new all-purpose statistics with computational tractability.
Neural networks can learn from higher-order cumulants efficiently, requiring quadratic samples.
problem Learning from higher-order cumulants in high-dimensional data.
method Spiked cumulant model, polynomial time algorithms, neural networks, random features.
result Neural networks require quadratic samples to learn from higher-order cumulants efficiently, while random features require more samples.
A new GAN loss function based on cumulant generating functions improves stability and robustness.
problem Improving the stability and performance of GANs.
method Cumulant GAN loss function based on variational R{é}nyi divergence.
result Cumulant GAN achieves linear convergence to Nash equilibrium and superior performance in image generation.
The paper calculates bounds for risk metrics and entropies under partial information constraints.
problem Analyzing risk metrics and entropies for unimodal, symmetric distributions with limited information.
method Develops lower and upper bounds for worst-case distortion riskmetrics and weighted entropy for unimodal, symmetric distributions with known mean and variance.
result Sharp upper bounds for distortion riskmetrics and weighted entropy for symmetric distributions.
Proposes a curriculum learning algorithm to maximize cumulative return in reinforcement learning.
problem Maximizing cumulative return in reinforcement learning tasks.
method Task sequencing algorithm maximizing cumulative return, using curriculum learning to minimize suboptimal actions.
result Significantly better performance on cumulative return maximization compared to metaheuristic algorithms.
Bayesian methods improve inference for cumulative probit models on large datasets.
problem Challenges in Bayesian inference for large cumulative probit models.
method Proposed scalable algorithms using Variational Bayes and Expectation Propagation.
result Superior computational performance and accuracy compared to MCMC.
The problem of an arbitrary truncated Levy flight description using the method of cumulant approach has been solved. The set of cumulants of the truncated Levy distribution given the assumption of arbitrary truncation has been found. The influence of truncation shape on the truncated Levy flight properties in the Gauss…
CENNSurv models cumulative effects of time-dependent exposures on survival outcomes.
problem Challenges in modeling cumulative effects of time-dependent exposures on survival outcomes.
method CENNSurv, a novel deep learning approach that captures dynamic risk relationships from time-dependent data.
result CENNSurv reveals multi-year lagged and short-term behavioral shifts in survival outcomes.
We define a new spectrum for compact length spaces and Riemannian manifolds called the "covering spectrum" which roughly measures the size of the one dimensional holes in the space. More specifically, the covering spectrum is a set of real numbers δ>0 which identify the distinct δ covers of the space. We investigat…
The subject of this paper is the relationship among the marked length spectrum, the length spectrum, the Laplace spectrum on functions, and the Laplace spectrum on forms on Riemannian nilmanifolds. In particular, we show that for a large class of three-step nilmanifolds, if a pair of nilmanifolds in this class has the …
The subject of this paper is the relationship among the marked length spectrum, the length spectrum, the Laplace spectrum on functions, and the Laplace spectrum on forms on Riemannian nilmanifolds. In particular, we show that for a large class of three-step nilmanifolds, if a pair of nilmanifolds in this class has the …
Paper calculates volatility distribution for cumulative production.
problem Volatility distribution for cumulative production.
method Generalizes study of volatility with arbitrary distribution function.
result Exact probability distribution function for volatility.
Method detects neural network equivalence via matrix ensembles and spectral analysis.
problem Detecting equivalence among different deep learning architectures.
method Generating Mixed Matrix Ensembles (MMEs) and matching to conjugate circular ensembles.
result Empirical evidence shows vanishing differences in spectral densities with long tail decay rates.
New algorithms minimize simple and cumulative regret in contextual bandits.
problem Minimizing simple and cumulative regret in contextual bandit settings.
method Proposed new algorithms using conformal arm sets (CASs).
result Near-optimal minimax guarantees for simple regret and state-of-the-art guarantees for cumulative regret.
Study the energy spectrum of metrics on surfaces and its relation to simple length spectrum.
problem Relate the energy spectrum to the simple length spectrum of metrics on surfaces.
method Analyze the energy spectrum of metrics on surfaces and their Teichmüller spaces, considering homotopy conditions.
result The energy spectrum determines the simple length spectrum under certain conditions.
Method determines credit transition matrix from cumulative default probabilities.
problem Quantifying changes in bond credit ratings.
method Setup an ill-posed, linear inverse problem with entropy minimization.
result Method successfully determines CTM from cumulative default probabilities.
New method calibrates classifier probabilities with guaranteed coverage.
problem Inaccurate probability estimates by classifiers in high-risk applications.
method Adaptive temperature scaling algorithm for conformal prediction.
result Improves calibration error measures and standard metrics across various tasks.
Paper converts quantiles to cumulative distribution functions to simplify risk measures.
problem Technical assumptions in risk measure calculations.
method Invention of converting integrated quantiles to integrated cumulative distribution functions.
result Avoids the need for probability density function existence.
The paper compares two spectrum definitions and finds stability in one modification.
problem Generalizing eigenvalues to arbitrary functionals with stability.
method Comparison of Gromov's homotopy significant spectrum and Krasnoskii spectrum, with a modified definition of the homotopy significant spectrum.
result The modified homotopy significant spectrum is stable, and Cheeger constant corresponds to Krasnoskii eigenvalue.
We introduce a new type of graphical model called a "cumulative distribution network" (CDN), which expresses a joint cumulative distribution as a product of local functions. Each local function can be viewed as providing evidence about possible orderings, or rankings, of variables. Interestingly, we find that the condi…
Proofs high-dimensional spectrum convergence of weighted sample covariance.
problem High-dimensional spectrum convergence of weighted sample covariance.
method Proposes a new, concise proof with stronger assumptions.
result Spectrum convergence proven for different weight distributions.
Study shows spectrum properties for specific Hadamard manifolds.
problem Spectrum properties of Hadamard manifolds.
method Absolute continuity and spectrum determination for two classes of Hadamard manifolds.
result Spectrum properties determined for specific Hadamard manifolds.
Develops regression trees for estimating cumulative incidence curves in competing risks.
problem Estimating cumulative incidence functions in competing risks settings.
method Uses augmented estimators of the Brier score risk to build and prune regression trees.
result Demonstrates the utility of the proposed methods through simulation studies and real data.
IPO optimizes reinforcement learning with constraints for better performance.
problem Maximizing long-term reward while satisfying cumulative constraints in decision problems.
method Interior-point Policy Optimization (IPO) using logarithmic barrier functions.
result IPO outperforms state-of-the-art baselines in reward maximization and constraint satisfaction.
A new model relaxes constraints on exponential dispersion models.
problem Tight conditions on cumulant function limit the class of exponential dispersion models.
method Introduces K-LED model with Legendre cumulant function and Bregman divergence guidance.
result The model allows for easier computation of mean parameter and includes various distributions.
Iterative method 'Concent' corrects spectrum bias in covariance matrices.
problem Consistent bias in the spectrum of covariance matrices.
method 'Concent' iterative algorithm.
result Corrects spectrum bias for small and moderate dimensions.
Paper proposes a new method to identify causal graphs with latent variables using higher-order cumulants.
problem Estimating causal directed acyclic graphs with latent confounders.
method Uses higher-order cumulants to identify causal structures among observed and latent variables.
result Validates the proposed algorithm through simulations and real-world data.
The paper identifies causal effects in latent variable models using higher-order cumulants.
problem Challenges in identifying causal effects in latent variable models with latent confounders.
method Using higher-order cumulants, the paper addresses two challenging setups: a single proxy variable and underspecified instrumental variables.
result Causal effects are identifiable with a single proxy or instrument.
We show power-scaling behaviors for fluctuations in share volume, which no other studies have so far done. After analyzing a database of the daily transactions for all securities listed on the Tokyo Stock Exchange, we selected 1050 large companies that each had an unbroken series of daily trading activity from January …
Proposes a new sampling method for online learning with cumulative oversampling.
problem Budgeted Influence Maximization in online learning.
method Cumulative Oversampling (CO) method for online learning.
result CO-based algorithm achieves comparable regret to UCB-based algorithms and performs similarly to Thompson Sampling.
Develops a new spectrum for annular links, recovering a transverse invariant at extreme gradings.
problem Understanding transverse link invariants in the annular setting.
method Constructs a stable homotopy type for annular links and defines a map to the Khovanov skein spectrum.
result At extreme gradings, the map from the Khovanov spectrum to the Khovanov skein spectrum recovers the cohomotopy transverse invariant.
The paper tackles non-cumulative objectives in reinforcement learning and proposes modifications to existing algorithms.
problem Optimizing objectives that are not naturally expressed as summations of rewards in various fields.
method The paper modifies the Bellman optimality equation to handle non-cumulative objectives by replacing summation with a generalized operation.
result The modified Bellman updates can converge to the globally optimal solution under certain conditions.
Constructs manifolds with specific spectral properties.
problem Spectral properties of Riemannian manifolds.
method Asymptotically hyperbolic manifolds with sharp curvature bounds.
result Embeds singular continuous spectrum into the essential spectrum of the Laplacian.
The spectrum of certain manifolds matches that of hyperbolic space if the bottom spectrum is maximal.
problem Investigating spectral rigidity of manifolds with Ricci bounded below and maximal bottom spectrum.
method Analyzing the spectrum of the Laplacian on manifolds with specific Ricci curvature bounds.
result The spectrum of the manifold coincides with that of hyperbolic space if the bottom spectrum is maximal.
Lower bounds for Hodge-Laplacian spectrum on orbifolds.
problem Finding bounds for the essential spectrum of Hodge-Laplacian.
method Deriving lower bounds for the essential spectrum of the Hodge-Laplacian on geometrically finite orbifolds and their suborbifolds.
result Lower bounds for the essential spectrum of the Hodge-Laplacian.
A machine learning approach for efficient spectrum sharing in distributed DSA networks.
problem Effective spectrum sharing among secondary users (SUs) and primary users (PUs) in a distributed network.
method Deep reinforcement learning (DRL) combined with reservoir computing (RC) for distributed spectrum access decisions.
result The RC-based spectrum access strategy significantly reduces collision chances and outperforms other methods.
Trapezoids uniquely identified by their Dirichlet Laplace spectrum.
problem Identifying trapezoids based on their spectral properties.
method Analyzing the Dirichlet Laplace spectrum of non-obtuse trapezoids.
result Non-obtuse trapezoids are uniquely determined by their Dirichlet Laplace spectrum.
In 2004, Sormani and Wei introduced the covering spectrum: a geometric invariant that isolates part of the length spectrum of a Riemannian manifold. In their paper they observed that certain Sunada isospectral manifolds share the same covering spectrum, thus raising the question of whether the covering spectrum is a sp…
New method corrects bias in datasets using cumulative distribution functions.
problem Varying domains and biased datasets lead to differences between training and target distributions.
method Empirical cumulative distribution function estimates of the target distribution, rigorously generalized.
result Method is more robust, not reliant on parameter tuning, and performs similarly to state-of-the-art techniques.
Survey on bottom of spectrum of Hodge Laplacian on complete noncompact Kähler manifolds
problem Bottom of the spectrum of Hodge Laplacian on complete noncompact Kähler manifolds
method Survey on Kähler hyperbolic manifolds and bounded symmetric domains
result Proposed several open problems