Develops a cumulant-based algorithm for optimizing investment portfolios.
problem Optimizing investment portfolios with low variability in non-Gaussian data.
method Alternating Least Square method applied to 2nd-6th cumulants of multidimensional random variables.
result The algorithm outperforms benchmarks and other methods during recent crashes.
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.
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.
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.
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.
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.
Data science enhances knot theory by analyzing invariant relations.
problem Understanding the complex relations between knot invariants.
method Topological data analysis applied to knot theory.
result New insights into long-standing conjectures about knots.
Investigates optimal investment strategies under CPT with risk-free and risky assets over multiple periods.
problem Optimal portfolio selection under CPT with constraints and stochastic benchmark.
method Numerical analysis of optimal CPT-investment strategies sensitivity to model parameters.
result Investment strategies under CPT are sensitive to model parameters.
New probabilistic CCA extensions with moment matching for multi-view models.
problem Estimating multi-view models with identifiability guarantees.
method Moment matching techniques, generalized covariance matrices, non-orthogonal joint diagonalization.
result Improved sample complexity and simplified algorithms.
Investors with CPT make optimal investment decisions in a market with transaction costs.
problem Optimal investment strategy under CPT in a market with transaction costs.
method Explicit solution for optimal investment strategy in two examples.
result Investment strategy is affected by transaction costs and risk aversion.
Paper proposes compressive ICA algorithms for ICA model.
problem Efficiently solving ICA model with reduced memory and computational complexity.
method Compressive learning approach to ICA model, proving existence of compressive ICA scheme, proposing two algorithms (IPG and ASD).
result Proposed algorithms achieve substantial memory gains over well-known ICA algorithms.
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.
New algorithms reduce regret in bandit problems with causal information.
problem Optimal intervention learning with causal background knowledge.
method Proposed C-UCB, C-TS, CL-UCB, and CL-TS algorithms.
result Improved cumulative regret bounds with causal information.
The paper analyzes worst-case distortion risk metrics and weighted entropy under partial information.
problem Analyzing worst-case distortion risk metrics and weighted entropy with limited information.
method General distributions, partial information (mean and variance), various entropies and risk measures.
result Provides worst-case results for distortion risk metrics and weighted entropy.
Improved BO algorithms reduce prediction error under Gaussian noise.
problem Reducing prediction error in Bayesian optimization with Gaussian noise.
method Established new prediction error bounds for Gaussian process under frequentist setting.
result Proved improved convergence rates of cumulative regret for GP-UCB and GP-TS.
Develops a method to analyze random-motion states in real-time using Lévy-parameters.
problem Analyzing the state of random-motion processes in real-time.
method Relates truncated cumulant-function of the fourth order with Lévian cumulant-function to derive explicit Lévy-parameters.
result Allows real-time analysis of random-motion states without cumbersome procedures.
The paper proposes a new method for clustering survival data using smoothed log-hazard trajectories.
problem Clustering survival data based on instantaneous risk dynamics.
method Functional Principal Component Analysis applied to B-spline smoothed log-hazard trajectories.
result The proposed method provides an interpretable representation of relative temporal risk dynamics.
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.
Improved cumulative regret for graph-based stochastic linear bandits.
problem Stochastic linear bandit problem with graph-structured preferences.
method Laplacian-regularized graph bandit algorithm with improved regret bounds.
result Single-user cumulative regret scales as i l d e O ( Ψ d T ) ilde{\mathcal{O}}(Ψd \sqrt{T}) i l d e O ( Ψ d T ) . The paper introduces a new method for detecting financial data outliers.
problem Detecting outliers in multivariate financial data.
method The approach uses the Cumulant Generating Function (CGF) to maximize projections on directions.
result The CGF maximization approach can be interpreted as an extension of principal component analysis.
Bayesian algorithms minimize cumulative regret in decentralized multi-agent bandits.
problem Minimizing cumulative regret in a decentralized multi-agent multi-armed bandit problem.
method Proposed decentralized Bayesian multi-armed bandit framework, including Thompson Sampling and Bayes-UCB algorithms.
result Regret scales logarithmically with constants matching those of an optimal centralized agent.
LinConTS improves regret and constraint violations in probabilistic linearly constrained bandits.
problem Maximizing cumulative reward under probabilistic linear constraints.
method LinConTS, a Thompson Sampling-based algorithm for bandits with linear constraints.
result LinConTS achieves O(log T) regret and constraint violations for suboptimal arms.
Optimistic algorithms and Thompson sampling use info-theory for better reinforcement learning.
problem Designing algorithms that balance exploration and exploitation in reinforcement learning.
method Integrating information-theoretic concepts into optimistic algorithms and Thompson sampling.
result Cumulative regret bound depends on uncertainty and quantifies prior information value.
Study geodesic properties of time series data using Wasserstein metric.
problem Modeling nonlinear time series with transport-based metrics.
method Generalized Wasserstein metric and signed cumulative distribution transforms.
result Geodesic properties provide added interpretability and robustness in time series classifiers.
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 1 / δ 1/δ 1/ δ with probability δ δ δ . This paper introduces a new metric, ULI, for RL that ensures both cumulative and instantaneous performance.
problem High-stakes applications require RL algorithms to avoid playing bad policies.
method Introduces uniform last-iterate (ULI) guarantee, a stronger metric capturing both cumulative and instantaneous performance.
result ULI directly implies near-optimal cumulative performance across various metrics, but not the other way around.
New framework extends ICA for non-independent variables, identifying pairwise mean independence.
problem Non-independent variables complicating ICA recovery.
method Algebraic recovery algorithm based on least-squares optimization over the orthogonal group.
result Pairwise mean independence is identifiable, robust to independence constraints.
Logarithmic regret achieved in Q-learning with positive gap.
problem Achieving logarithmic cumulative regret in Q-learning with positive sub-optimality gap.
method Optimistic Q-learning with logarithmic regret bound.
result Logarithmic cumulative regret bound proven for optimistic Q-learning.
Bayesian optimization improved for biased data.
problem Adversarial bias in observations, especially hidden confounders.
method Reduction to dueling bandits, information-directed sampling (IDS).
result First efficient kernelized algorithm with regret guarantees.
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 …
Bayesian optimization in one dimension achieves O ( T log T ) O(\sqrt{T\log T}) O ( T log T ) regret.
problem Optimizing a function in one dimension with Gaussian process prior and noise.
method Theoretical analysis of Gaussian process and Gaussian sampling noise.
result Cumulative regret up to time T T T is O ( T log T ) O(\sqrt{T\log T}) O ( T log T ) under mild assumptions. 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…
In this work, a statistical analysis of the distribution of daily fluctuations of the IPC, the Mexican Stock Market Index is presented. A sample of the IPC covering the 13-year period 04/19/1990 - 08/21/2003 was analyzed and the cumulative probability distribution of its daily logarithmic variations studied. Results sh…
Paper proposes a framework for reliable off-policy evaluation in reinforcement learning.
problem Quantifying uncertainty in off-policy estimates for safe deployment of target policies.
method Distributionally robust optimization for creating confidence bounds.
result Non-asymptotic and asymptotic guarantees for robust cumulative reward estimates.
The paper addresses evaluating survival predictions using discrimination measures, finding a robust method to convert distributions to risks.
problem Evaluating survival distribution predictions with discrimination measures is challenging and often leads to unfair comparisons.
method The paper surveys existing methods and recommends summing over the predicted cumulative hazard as the most robust method to convert distributions to risks.
result Summing over the predicted cumulative hazard is the most robust method to convert distribution predictions to risk predictions.
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…
New method identifies latent variables with causal dependencies from observed data.
problem Identify latent variables with causal relationships from observed data.
method Linear causal disentanglement via higher-order cumulants, with perfect and soft interventions.
result Recovery of parameters via coupled tensor decomposition and polynomial equations.
This paper analyzes risk perception and aversion in decision-making.
problem Understanding and quantifying risk perception and aversion in decision-making.
method Theoretical analysis and generalized CPT-utility function development.
result A generalized CPT-utility function that captures risk perception and aversion.
The paper calculates European option prices under a generalized skew normal distribution.
problem European option pricing under a generalized skew normal distribution.
method Proved existence of martingale measure, derived explicit option pricing formula, applied numerical methods.
result Explicit expressions for European option prices are derived.
The paper extends and applies a new shrinkage prior in Bayesian factor analysis.
problem Estimating the number of factors in sparse Bayesian factor analysis.
method Introduces and extends a generalized cumulative shrinkage process (CUSP) prior.
result Exchangeable spike-and-slab shrinkage priors imply increasing shrinkage as the column index increases.
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.
SurvLIME-KS improves survival model explanations robustly.
problem Improving explanations of unreliable survival models.
method SurvLIME-KS combines Cox proportional hazards model and Kolmogorov-Smirnov bounds for robust optimization.
result SurvLIME-KS minimizes average distance and maximizes distance in approximating cumulative hazard functions.
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.
Paper proposes an efficient AL-GP method for CDF/CCDF estimation in UQ.
problem Estimating full probability distribution in forward UQ analysis.
method Active learning-based Gaussian process (AL-GP) metamodelling method.
result Efficient estimation of CDF/CCDF without explicit discretization.
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.
New algorithm minimizes regret in stochastic bandits.
problem Minimizing cumulative regret in stochastic bandits.
method Introduces anytime OCUCB algorithm with strong regret guarantees.
result Upper and lower bounds nearly match for new algorithm.
The question of the optimality of Thompson Sampling for solving the stochastic multi-armed bandit problem had been open since 1933. In this paper we answer it positively for the case of Bernoulli rewards by providing the first finite-time analysis that matches the asymptotic rate given in the Lai and Robbins lower boun…