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…
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48 results for “Cumulant Conditions”
Conventional multiclass conditional probability estimation methods, such as Fisher's discriminate analysis and logistic regression, often require restrictive distributional model assumption. In this paper, a model-free estimation method is proposed to estimate multiclass conditional probability through a series of cond…
The paper revisits expected signatures in semimartingale models, providing new formulae and simplifying complexity.
problem Computing expected signatures in semimartingale models.
method Revisits and provides new formulae for computing expected signatures in a general semimartingale setting.
result Log-transform of expected signatures simplifies complexity, leading to signature cumulants.
Derives a general derivative identity for conditional mean in Gaussian noise.
problem Understanding conditional mean in Gaussian noise channels.
method Derives a general derivative identity for the conditional mean of given in a Markov chain .
result Provides a unifying view of conditional mean identities and derives new ones.
The stochastic multi-armed bandit (MAB) problem is a common model for sequential decision problems. In the standard setup, a decision maker has to choose at every instant between several competing arms, each of them provides a scalar random variable, referred to as a "reward." Nearly all research on this topic consider…
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.
Directed acyclic graphs (DAGs) are a popular framework to express multivariate probability distributions. Acyclic directed mixed graphs (ADMGs) are generalizations of DAGs that can succinctly capture much richer sets of conditional independencies, and are especially useful in modeling the effects of latent variables im…
Inexact acquisition solutions in BO lead to sublinear cumulative regret.
problem Inexact maximization of acquisition functions in Bayesian optimization.
method Define inaccuracy measure, establish cumulative regret bounds for GP-UCB and GP-TS.
result Inexact BO algorithms can achieve sublinear cumulative regret under appropriate inaccuracy conditions.
Deep conditional transformation models unify interpretable and complex predictors.
problem Challenging to learn conditional CDFs in high-dimensional settings.
method Unified deep learning framework for interpretable and complex predictors.
result Efficacy demonstrated through numerical experiments and applications.
This paper studies continuum-armed bandits under Besov smoothness conditions and derives minimax rates.
problem Optimizing an unknown function with limited evaluations.
method Studies continuum-armed bandits under Besov smoothness conditions and derives minimax rates.
result Minimax rates over Besov spaces are identical to those over the smallest Hölder space into which Besov spaces embed.
The study examines higher-order modern portfolio theory with complex critical points and feasible portfolio variety.
problem Understanding the complex critical points and feasible portfolio variety in higher-order modern portfolio theory.
method Established genericity conditions for utility functions with higher-order cumulants, analyzed discriminant loci, and determined the dimension and degree of the feasible portfolio variety.
result The utility function has a constant number of complex critical points under genericity conditions, and the feasible portfolio variety has a determined dimension and degree.
The paper studies empirical processes from nearest neighbors in regression.
problem Estimating conditional cumulative distribution functions and local linear regression.
method Uniform central limit theorem and non-asymptotic bound under local bracketing entropy and uniform entropy numbers.
result Gaussian limit of empirical process with simple covariance.
New method identifies causal structure in count data using cumulants and path analysis.
problem Challenges in discovering causal structure from count data, especially due to non-identifiability.
method Poisson Branching Structural Causal Model (PB-SCM) with path analysis using high-order cumulants.
result Causal order is identifiable under specific conditions in PB-SCM using cumulant information.
This paper analyzes OCBA algorithms' convergence rates for DEDS optimization.
problem Optimizing discrete-event dynamic systems with limited computing resources.
method Characterizes convergence rates of two OCBA algorithms under different performance measures.
result OCBA algorithms achieve optimal convergence rates under probability of correct selection and expected opportunity cost measures.
Nonparametric neural-network estimation of current-status data
problem Estimation of conditional cumulative distribution function with current-status data
method Neural-network sieve maximum likelihood estimator
result Explicit convergence rate for Hölder smoothness
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.
Bregman-divergence-guided Legendre exponential dispersion model with finite cumulants (K-LED)math.ST
Exponential dispersion model is a useful framework in machine learning and statistics. Primarily, thanks to the additive structure of the model, it can be achieved without difficulty to estimate parameters including mean. However, tight conditions on cumulant function, such as analyticity, strict convexity, and steepne…
This paper analyzes regret bounds for Gaussian process Thompson sampling.
problem Analyzing the performance of Gaussian process Thompson sampling (GP-TS) in Bayesian optimization.
method The paper derives several regret bounds for GP-TS, including a lower bound, upper bounds on the second moment of cumulative regret, expected lenient regret, and improved cumulative regret.
result The paper provides improved regret upper bounds for GP-TS, showing that it suffers from a polynomial dependence on with probability .
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 …
Significance of log-periodic signatures in cumulative noisecond-mat.stat-mech
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…
New method identifies structural parameters without assuming uncorrelated errors.
problem Identifying structural parameters in simultaneous equation models.
method Exploits higher-order cumulant restrictions, not requiring uncorrelated errors.
result Simple diagonality condition on th-order cumulants identifies structural parameter matrix.
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.
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.
Cumulant GANcs.LG
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 develops methods to predict the probability of achieving a user goal in a task, ensuring the system alerts when the probability falls below a threshold.
problem Ensuring an autonomous system achieves the user's goal with calibrated probability estimates.
method Invertible conformal prediction using Probability-space Conformalized Quantile Regression (PCQR) to produce well-calibrated conditional prediction intervals.
result The method produces well-calibrated probabilities that the cumulative reward will fall within a user-specified target interval, with finite-sample guarantees.
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.
Directly estimates CQC, improving interpretability and accuracy.
problem Inability to model and interpret CQC due to inversion issue.
method Direct doubly robust estimation of CQC without inversion.
result Improved estimation accuracy and interpretability.
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…
Efficient estimation of weighted cumulative treatment effects by double/debiased machine learningstat.ME
Proposes efficient estimators for weighted cumulative treatment effects in observational studies.
problem Inconsistent and inefficient estimators due to model misspecification and lack of overlap.
method Double/debiased machine learning for weighted cumulative causal effects.
result Proposed estimators are consistent, asymptotically linear, and reach semiparametric efficiency bounds.
Within the framework of the cumulative prospective theory of Kahneman and Tversky, this paper considers a continuous-time behavioral portfolio selection problem whose model includes both running and terminal terms in the objective functional. Despite the existence of S-shaped utility functions and probability distortio…
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.
A new model uses neural networks to efficiently learn multivariate temporal point processes.
problem Efficiently modeling multivariate temporal point processes with low parameter complexity.
method Modeling the cumulative hazard function with neural networks for each variate.
result The proposed model achieves state-of-the-art performance on data fitting and event prediction tasks.
The objective in a traditional reinforcement learning (RL) problem is to find a policy that optimizes the expected value of a performance metric such as the infinite-horizon cumulative discounted or long-run average cost/reward. In practice, optimizing the expected value alone may not be satisfactory, in that it may be…
Localized Debiased Machine Learning: Efficient Inference on Quantile Treatment Effects and Beyondstat.ML
We consider estimating a low-dimensional parameter in an estimating equation involving high-dimensional nuisances that depend on the parameter. A central example is the efficient estimating equation for the (local) quantile treatment effect ((L)QTE) in causal inference, which involves as a nuisance the covariate-condit…
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.
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.
TVBO optimizes time-varying functions with asymptotically vanishing regret.
problem Understanding the asymptotic performance of TVBO for time-varying black-box functions.
method Provided upper and lower bounds for cumulative regret of TVBO algorithms.
result TVBO algorithms can achieve asymptotically vanishing regret under certain conditions.
A new neural network model for ordinal regression.
problem Ordinal regression with non-proportional odds.
method Interpretable neural network for both continuous and discrete responses, training a non-linear neural network as a coefficient function.
result NPOM preserves interpretability while offering flexibility.
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.
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.
Unified probabilistic gradient boosting for entire conditional distribution modeling.
problem Creating accurate probabilistic forecasts from regression tasks.
method Unified probabilistic gradient boosting framework using XGBoost and LightGBM, modeling conditional moments or CDF via Normalizing Flows.
result Achieves state-of-the-art forecast accuracy.
New framework finds periodic policies in reset-free MDPs with sublinear regret.
problem Reset-free reinforcement learning with unknown dynamics and terminal law constraints.
method Periodic framework, periodic policies, periodic regret.
result First non-asymptotic guarantees for reset-free learning in multi-agent settings.
QSurv models survival data without discretization, achieving high accuracy.
problem Intractable likelihood estimation for continuous-time survival models.
method QSurv uses numerical quadrature for cumulative hazard approximation and time-conditioned low-rank adaptation.
result QSurv achieves competitive predictive performance and interpretable hazard patterns.
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.
Scaling Law for the Distribution of Fluctuations of Share Volumecond-mat.stat-mech
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 …