Paper identifies unobserved variables from observable data.
problem Missing variables in empirical studies.
method Function mapping from observables to unobservables based on joint distribution.
result Uniqueness of latent values in each observation.
Neural Empirical Bayes estimates source distributions from noisy simulations.
problem Estimating source distributions from noisy, simulated data.
method Uses neural density estimators to estimate a prior or source distribution over uncorrupted samples, then performs posterior inference.
result Recovering ground truth source distributions up to symmetries.
Extends PD-NJ-ODE to noisy observations and dependent observation times.
problem Predicting continuous-time stochastic processes with irregular and noisy observations.
method Extends PD-NJ-ODE to handle conditional independence and noisy observations.
result Theoretical guarantees and empirical examples for handling noisy observations and dependent observation times.
Empirical mode modeling improves state-space analysis of noisy data.
problem Analyzing nonlinear systems with noisy data.
method Combining empirical mode decomposition with empirical dynamic modeling.
result Empirical mode modeling enhances state-space representations in noisy data.
Optimal algorithms for online convex optimization with missing sub-gradient observations.
problem Online convex optimization with noisy or missing sub-gradient observations.
method Adaptive algorithms using sub-gradient descent with minimax optimal regret guarantees.
result Achieves tight minimax optimal regret bounds with empirical property estimation.
Improved hedging strategy for SABR model options.
problem Inaccurate conventional SABR delta hedging.
method Theoretical justification of Bartlett's delta.
result Bartlett's delta provides more accurate hedging.
Empirical Bayes method improves Gaussian sequence model inference.
problem Estimating parameters in correlated Gaussian sequence models.
method Maximum Composite Marginal Likelihood (CML) estimator, leveraging geometric Brascamp-Lieb inequality.
result CML estimator converges at rate \( n_*^{-1/2} \) in weighted Hellinger distance.
New EB methods handle correlated observations in the Normal Means problem.
problem Handling correlations in the Normal Means problem.
method Developed new EB methods based on Schwartzman's theory.
result New methods compare favorably with other methods in FDR control.
We perform an extensive empirical analysis of scaling properties of equity returns, suggesting that financial data show time varying multifractal properties. This is obtained by comparing empirical observations of the weighted generalised Hurst exponent (wGHE) with time series simulated via Multifractal Random Walk (MR…
We present an empirical study of the first passage time (FPT) of order book prices needed to observe a prescribed price change Delta, the time to fill (TTF) for executed limit orders and the time to cancel (TTC) for canceled ones in a double auction market. We find that the distribution of all three quantities decays a…
Empirical study shows removing neural parameter symmetries impacts model performance.
problem Understanding the impact of neural parameter symmetries on model performance.
method Developed two methods to reduce parameter space symmetries in neural networks.
result Removing parameter symmetries can lead to faster and more effective Bayesian neural network training.
We establish conditions for maximum likelihood consistency in time series models.
problem Invertibility conditions often fail in empirical observation-driven models.
method Derive weaker conditions for maximum likelihood consistency.
result Consistency of maximum likelihood estimator holds for various models.
The paper analyzes the tradeoff between bias and overfitting in reinforcement learning with partial observability.
problem Analyzing the tradeoff between asymptotic bias and overfitting in reinforcement learning with partial observability.
method Theoretical analysis and empirical illustration using truncated history of observations and function approximators.
result A smaller state representation decreases the risk of overfitting, but potentially increases asymptotic bias.
New empirical process bounds reveal trade-off between dependence and complexity in nonparametric learning.
problem Understanding generalization in nonparametric learning with temporal dependencies.
method Developed bounds on expected supremum of empirical processes under β/ρ-mixing assumptions. result Achieved rates similar to i.i.d. setting under long-range dependence with complex function classes.
Transformers can learn Markov processes with constant depth, surprising results.
problem Understanding how transformers learn context in Markov processes.
method Empirical study and theoretical analysis of attention-based transformers on Markov data.
result Transformers with constant depth can achieve low test loss on Markov sequences, matching empirical and theoretical findings.
New method combines experimental and observational data for causal inference.
problem Combining internal validity of experiments and larger sample sizes of observations.
method Empirical risk minimization (ERM) framework with cross-validation.
result Efficacy and reliability demonstrated on real and synthetic data.
The paper tackles fairness in machine learning by incorporating it into empirical risk minimization.
problem Ensuring fairness in classifier outcomes by preventing sensitive variables from unfairly influencing results.
method Empirical risk minimization with a fairness constraint that maintains approximately constant conditional risk with respect to the sensitive variable.
result The approach is statistically consistent and can be applied to kernel methods and linear models with simple preprocessing steps.
A new SGD framework reduces empirical risk by favoring higher loss observations.
problem Minimizing empirical risk in machine learning problems.
method Develops a biased gradient estimator for stochastic optimization.
result Minimizes an ordered modification of the empirical average loss.
We study some properties of eigenvalue spectra of financial correlation matrices. In particular, we investigate the nature of the large eigenvalue bulks which are observed empirically, and which have often been regarded as a consequence of the supposedly large amount of noise contained in financial data. We challenge t…
The paper improves generative models to avoid replicating observed examples.
problem Improving generative models to avoid replicating observed examples.
method Theoretical insights into the Wasserstein GAN, constrained to left-invertible push-forward maps, generating distributions that avoid replication and significantly deviate from the empirical distribution.
result Left-invertibility achieves this without compromising statistical optimality.
Framework for optimizing search engine rankings using observational data.
problem Optimizing ranking policies for search engines using limited observational data.
method Formulated expected reward optimization problem, estimated context value distribution, trained ranking policy via Bayesian inference.
result Demonstrated trade-offs in ranking policies trained on empirical reward estimates.
Robust RL with learned optimal adversary improves agent performance under adversarial state observations.
problem Ensuring reinforcement learning agents' robustness against adversarial perturbations of state observations.
method Proposed a framework of alternating training with learned adversaries (ATLA) to find optimal adversarial policies and enhance agent robustness.
result ATLA achieves state-of-the-art performance under strong adversaries in continuous control environments.
Estimates Heston SDE parameters from observable realized volatilities.
problem Estimating parameters of Heston SDEs from observable data.
method Constructs estimators from empirical moments of realized volatilities over sliding windows.
result Explicit bounds for the convergence of realized volatilities to true volatilities.
New method for PU learning with instance-dependent propensity scores.
problem Learning from positive and unlabeled data with instance-dependent labeling.
method Empirical risk minimization of joint risk function, alternating optimization of posterior probability and propensity score.
result The method achieves comparable or better performance than state-of-the-art methods.
Study learns state representations from observations for control, proving guarantees.
problem Learning state representations from high-dimensional observations for control.
method Cost-driven approach, learning latent state model to predict costs.
result Proves finite-sample guarantees for near-optimal state representation and controller.
We present results about financial market observables, specifically returns and traded volumes. They are obtained within the current nonextensive statistical mechanical framework based on the entropy Sq=k1−q1−i=1∑Wpiq(q∈ℜ) ($S_{1} \equiv S_{BG}=-k\sum\limits_{i=1}^{W}p_{i} \l…
Efficient learning with robust gradient descent reduces resource usage.
problem Learning from noisy or heavy-tailed data requires many observations.
method Constructs a robust approximation of the risk gradient for iterative learning.
result Shows that the proposed procedure learns more efficiently with less resources.
Study sharp convergence rates of empirical UOT for spatio-temporal point processes.
problem Statistical analysis of UOT for spatio-temporal point processes.
method Empirical plug-in estimators for Kantorovich-Rubinstein distance between intensity measures.
result Sharp convergence rates of empirical UOT in terms of intrinsic dimensions of measures.
Machine learning identifies math sequences based on empirical laws.
problem Identifying interesting mathematical structures.
method Extract features from integer sequences using Benford's and Taylor's laws; experiment with classifiers.
result Machine learning can identify various mathematical properties in sequences.
The paper provides bounds for the empirical angular measure and applies them to improve statistical learning in extreme regions.
problem Estimating the angular measure in high-dimensional data with different distributions.
method Established bounds for the maximal deviations of the empirical angular measure from the true measure, using rank transformation and analyzing the most extreme observations.
result The bounds provide performance guarantees for statistical learning procedures in extreme regions, such as binary classification and anomaly detection.
New RL algorithms use lookahead info to maximize rewards.
problem RL in unknown environments without lookahead info.
method Planning using empirical reward and transition distributions.
result Achieves tight regret compared to lookahead info.
We derive a continuous time model for the joint evolution of the mid price and the bid-ask spread from a multiscale analysis of the whole limit order book (LOB) dynamics. We model the LOB as a multiclass queueing system and perform our asymptotic analysis using stylized features observed empirically. We argue that in t…
Detect changes in noisy dynamical systems using empirical approximations and finite-sample bounds.
problem Change detection in noisy dynamical systems
method Partition-based empirical approximations and finite-state stationary distribution stability
result Finite-sample bound for empirical stationary density
Study describes how national credit operations emerge from subnational data.
problem Understanding national credit dynamics from subnational data.
method Proposed diffusion process to aggregate subnational credit operations.
result National credit dynamics accurately described with proposed model.
Empirical observations of CNN invertibility explained with a mathematical model.
problem Understanding why Convolutional Neural Networks (CNNs) are approximately invertible.
method Developed a mathematical model of sparse signal recovery consistent with random-weight CNNs, connecting to model-based compressive sensing.
result CNNs trained with random weights are consistent with the mathematical model and can be used for reasonable image reconstruction.
Paper uses learned summary statistics for Bayesian inference with difficult likelihood functions.
problem Difficult to obtain exact likelihood function for observation data and simulation model.
method Simulation-based inference with learned summary statistics, using Cressie-Read discrepancy criterion.
result Effective inference performed over selected sample sets of observation data.
A new method for optimizing hyperparameters using conformalized quantile regression.
problem Optimizing hyperparameters with strong assumptions about noise.
method Conformalized quantile regression for more realistic modeling.
result Quicker convergence on empirical benchmarks.
Empirical Gaussian Processes learn flexible priors from data.
problem Limited effectiveness of standard Gaussian process kernels.
method Estimate mean and covariance functions empirically from data.
result Empirical GPs converge to closest GP to real data generating process.
The paper examines how timing of observations affects causal discovery methods.
problem The sensitivity of causal discovery methods to mismatched observation timing.
method Empirical and theoretical analysis of classical and recent causal discovery methods.
result Causal discovery methods are sensitive to sampling rate and window length.
This paper extends IRL to handle summarized data without specific assumptions.
problem Handling summarized data in inverse reinforcement learning.
method Developed algorithms for exact and approximate inference without assuming specific structure of summarizing function.
result Full posterior inference is possible for estimating parameters in challenging situations.
We study the relaxation dynamics of a financial market just after the occurrence of a crash by investigating the number of times the absolute value of an index return is exceeding a given threshold value. We show that the empirical observation of a power law evolution of the number of events exceeding the selected thre…
Study price responsiveness in electricity demand using empirical data.
problem Limited effectiveness of classical economic theories in real-time retail pricing.
method Dynamic modeling of hybrid Hammerstein model with delay and linear ARX model.
result Electricity consumption has distinct responses to moderate and high prices with a time delay.
Study on double descent behavior in two-layer neural networks for binary classification.
problem Understanding the double descent phenomenon in model test error.
method Two-layer neural network with ReLU activation for binary classification. Quantified model size by sample-to-dimension ratio. Empirical risk minimization using Convex Gaussian Min Max Theorem.
result Observed and investigated the double descent behavior of model test error.
New algorithm improves reinforcement learning from partial observations.
problem Inferior performance of algorithms in real-world reinforcement learning due to partial observability.
method Representation-based approach to POMDPs, leading to a tractable algorithm.
result Empirically demonstrates superior performance with partial observations.
Paper tackles multi-view reinforcement learning with two methods.
problem Decision making with shared dynamics and different observation models.
method Observation augmentation and cross-view policy transfer.
result Reductions in sample complexities and computational time for multi-view environments.
Generative models improve causal effect estimation from observational data.
problem Estimating causal effects from observational data, especially when confounding factors are present.
method Proposes a progressive sequence of Variational Auto-Encoder models to learn underlying factors and causal effects.
result Empirical results show superior performance compared to state-of-the-art approaches.
This paper is a contribution to the Proceedings of the Workshop Complexity, Metastability and Nonextensivity held in Erice 20-26 July 2004, to be published by World Scientific. We propose a generalization to Merton's model for evaluating credit spreads. In his original work, a company's assets were assumed to follow a …
This paper studies the partial estimation of Gaussian graphical models from high-dimensional empirical observations. We derive a convex formulation for this problem using ℓ1-regularized maximum-likelihood estimation, which can be solved via a block coordinate descent algorithm. Statistical estimation performance …