Kurtosis is seen as a measure of the discrepancy between the observed data and a Gaussian distribution and is defined when the 4th moment is finite. In this work an empirical study is conducted to investigate the behaviour of the sample estimate of kurtosis with respect to sample size and the tail index when applied to…
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48 results for “index sampling”
Abstract reviews algorithms for multi-index models, focusing on polynomial-time methods and their limitations.
problem Estimating the index space in multi-index models efficiently and accurately.
method Polynomial-time algorithms in Gaussian space, nonparametric gradient estimation, and neural network fitting.
result A gap exists between computationally efficient methods and information-theoretical minimum.
Improved SGD learning for single index models reduces sample complexity.
problem Learning a single index model with optimal sample complexity.
method Using smoothed loss in online SGD to reduce sample complexity.
result Online SGD with smoothed loss achieves optimal sample complexity of .
The NIG model outperforms others in pricing S&P 500 index options.
problem Analyzing and pricing S&P 500 index options with Lévy jumps.
method Parameter estimation using SSE method for various models (BS, SV, SVJ, non-IID, Lévy (GH, NIG, CGMY)).
result NIG model outperforms other models in both in-sample and out-of-sample periods.
Paper presents an efficient exploration method for reinforcement learning.
problem Efficient exploration in reinforcement learning with uncertainty quantification.
method Parameterized Indexed Value Function (PIV) using index sampling.
result Proves the regret bound for learning PIV in a tabular setting and proposes PINs for computational learning.
The paper explores when linear system identification is hard or easy, especially for under-actuated systems.
problem Statistical hardness of learning linear systems, especially under-actuated or under-excited systems.
method Using tools from minimax theory and recent statistical tools for finite sample analysis of system identification.
result The controllability index of linear systems affects the sample complexity of identification, making some systems hard to learn.
Enhanced indexation uses equity and index options for better performance.
problem Improving portfolio performance through enhanced indexation.
method Integrating index options into an enhanced indexation strategy based on second-order stochastic dominance.
result Introducing option strategies in enhanced indexation leads to improved out-of-sample performance.
Bank transactions help predict macroeconomic indexes faster and more accurately.
problem Lag in macroeconomic index availability and autoregressive models' limitations in complex scenarios.
method Use financial transactions data to estimate macroeconomic indexes using neural networks and smart sampling.
result Neural network approach outperforms baseline methods on hand-crafted features based on transactions.
Asset pre-selection for a cardinality constrained index tracking portfolio with optional enhancementq-fin.PM
The paper optimizes asset selection for index trackers and enhanced trackers with varying cardinality constraints.
problem Optimizing asset selection for index trackers and enhanced trackers with cardinality constraints.
method Divided into two steps: asset pre-selection and asset weight estimation. Used eight pre-selection procedures with different combinations of selection methods and regression types.
result Out-of-sample tracking errors are roughly proportional to 1/sqrt(cardinality). OLS is more effective than LAD, BE marginally more effective than FS, and (n) marginally more effective than (c).
New neural networks learn single-index models efficiently.
problem Learning low-dimensional structure in high-dimensional data.
method Shallow neural networks with frozen biases, studied via gradient flow.
result Generalization guarantees match near-optimal sample complexity.
Kernelized bandit algorithm tackles adaptive contextual bandits with single-index models.
problem Adaptive contextual bandits with single-index models and unknown link functions.
method Kernelized ε-greedy algorithm combining Stein-based index estimation and kernel ridge regression for reward functions.
result Unified framework for simultaneous learning and inference in single-index contextual bandits.
The Generative Leap: Sharp Sample Complexity for Efficiently Learning Gaussian Multi-Index Modelscs.LG
Study efficient estimation of hidden subspaces in Gaussian Multi-index models.
problem Estimating hidden subspaces in Gaussian Multi-index models with low-dimensional projections.
method Introduced the generative leap exponent and developed an agnostic sequential estimation procedure using spectral U-statistics.
result Achieved optimal sample complexity of $n=Θ(d^{1 \vee \k/2})$ for efficient estimation.
This paper investigates the problem of recovering missing samples using methods based on sparse representation adapted especially for image signals. Instead of -norm or Mean Square Error (MSE), a new perceptual quality measure is used as the similarity criterion between the original and the reconstructed images. T…
New algorithm reduces sample complexity for omnipredictors of SIMs.
problem Learning optimal predictors for various loss functions.
method Sharp analysis of Isotron algorithm for agnostic learning.
result Improved sample complexity to for bi-Lipschitz link functions.
By adopting Multifractal detrended fluctuation (MF-DFA) analysis methods, the multifractal nature is revealed in the high-frequency data of two typical indexes, the Shanghai Stock Exchange Composite 180 Index (SH180) and the Shenzhen Stock Exchange Composite Index (SZCI). The characteristics of the corresponding multif…
THRML uses energy-based models for index tracking, reducing portfolio tracking error and improving returns.
problem NP-hard combinatorial optimization in portfolio optimization under cardinality constraints.
method THRML reformulates index tracking as probabilistic inference on an Ising Hamiltonian, using GPU-accelerated block Gibbs sampling.
result THRML achieves 4.31 percent annualized tracking error compared to 5.66-6.30 percent for baselines, with 128.63 percent total return.
This work improves online SGD's sample complexity for multi-index models by considering higher-order terms.
problem Suboptimal sample complexity for learning multi-index models using online SGD.
method Focus on both second- and higher-order terms to improve sample complexity.
result Online SGD achieves samples for multi-index models.
SGD shows distinct phases in learning single-index models, achieving optimal sample complexity and regret.
problem Learning single-index models with SGD in adaptive data settings.
method Stochastic gradient descent (SGD) with an optimal learning rate schedule.
result SGD achieves near-optimal sample complexity and regret guarantees across both burn-in and learning phases.
Training a neural network for a classification task typically assumes that the data to train are given from the beginning. However, in the real world, additional data accumulate gradually and the model requires additional training without accessing the old training data. This usually leads to the catastrophic forgettin…
Full-batch GD outperforms one-pass SGD in learning a single-index model with quadratic activation.
problem Learning a single-index model with quadratic activation using gradient descent.
method Full-batch gradient descent compared to one-pass stochastic gradient descent (SGD) on a correlation loss.
result Full-batch GD requires only samples for strong recovery, while one-pass SGD requires samples.
Accurate solution of the Index Tracking problem with a hybrid simulated annealing algorithmcond-mat.stat-mech
Hybrid SA algorithm optimizes index tracking for large indices.
problem Optimizing index tracking for large indices with financial constraints.
method Hybrid simulated annealing algorithm.
result Algorithm finds optimal solutions for past and future returns.
Neural networks can achieve optimal sample complexity for learning single-index models.
problem Achieving optimal computational-statistical tradeoff in learning Gaussian single-index models.
method Unified gradient-based algorithm for training a two-layer neural network, adaptable to various loss and activation functions.
result Sample complexity of matches the SQ lower bound up to a polylogarithmic factor.
A new model tracks indices without rebalancing, solving NP-hard problems.
problem Tracking indices without rebalancing and minimizing deviations.
method Metaheuristic algorithms and local branching for solving mixed integer linear programming.
result The heuristic generates portfolios that outperform commercial solvers in both in-sample and out-of-sample data.
Extensions to given-data Sobol' index estimators for large models.
problem Efficiently compute Sobol' indices for models with many inputs.
method General definition, streaming algorithm, heuristic filtering.
result Comparable accuracy and lower memory usage for large models.
Single index model is a powerful yet simple model, widely used in statistics, machine learning, and other scientific fields. It models the regression function as , where a is an unknown index vector and x are the features. This paper deals with a nonlinear generalization of this framework to allow for a regre…
Study shows computational and statistical gaps in Gaussian Single-Index Models.
problem Statistical and computational trade-offs in high-dimensional regression problems.
method Analysis of SQ and LDP frameworks, partial-trace algorithm.
result Computational algorithms require significantly more samples than information-theoretic limits.
Study shows time-varying stock returns across economic states.
problem Equity premium predictability varies by economic state.
method State-switching predictive regression using yield curve slope.
result The Aligned Economic Index improves stock return prediction.
In this paper, we establish the stochastic ordering of the Gini indexes for multivariate elliptical risks which generalized the corresponding results for multivariate normal risks. It is shown that several conditions on dispersion matrices and the components of dispersion matrices of multivariate normal risks for the m…
I analyse the frequentist regret of the famous Gittins index strategy for multi-armed bandits with Gaussian noise and a finite horizon. Remarkably it turns out that this approach leads to finite-time regret guarantees comparable to those available for the popular UCB algorithm. Along the way I derive finite-time bounds…
Paper tackles missing data in irregularly-sampled time series.
problem Modeling irregularly-sampled time series data.
method Encoder-decoder framework based on variational autoencoders and generative adversarial networks.
result Models achieve competitive or better classification results on irregularly-sampled multivariate time series.
The paper analyzes the sliding regret of stochastic bandit algorithms.
problem Measuring the one-shot behavior of no-regret algorithms in stochastic bandits.
method Introducing sliding regret to measure the worst pseudo-regret over a time-window.
result Randomized methods have optimal sliding regret, while index policies have the worst possible sliding regret.
Study spectral estimators for multi-index models to recover low-dimensional signal subspaces.
problem Recovering low-dimensional signal subspaces in multi-index models.
method Spectral estimators for multi-index models.
result Precise asymptotic characterization of spectral methods' performance, revealing a phase transition for weak recovery.
The Hype Index measures media attention to equities using NLP.
problem Quantifying media attention to equities for volatility analysis.
method Constructs News Count-Based and Capitalization Adjusted Hype Indices using NLP.
result The Hype Index family provides valuable tools for stock volatility analysis.
Study uses neural nets to learn multi-index models in high dimensions, reducing complexity.
problem Learning multi-index models in high-dimensional data.
method Mean-field Langevin dynamics with neural networks.
result Effective dimension controls sample and computational complexity, potentially reducing it.
Unified framework predicts S&P500 index direction using transfer learning and causal graph.
problem Predicting the movement of financial indices like S&P500.
method Transfer learning, causal graph, multidisciplinary knowledge, VAE network.
result 74.3% accuracy, 67% F1-score, 0.42 Matthew correlation on 12 years test period.
We propose sequenced-replacement sampling (SRS) for training deep neural networks. The basic idea is to assign a fixed sequence index to each sample in the dataset. Once a mini-batch is randomly drawn in each training iteration, we refill the original dataset by successively adding samples according to their sequence i…
In this paper, we study the missing sample recovery problem using methods based on sparse approximation. In this regard, we investigate the algorithms used for solving the inverse problem associated with the restoration of missed samples of image signal. This problem is also known as inpainting in the context of image …
The Stochastic Volatility (SV) model and its variants are widely used in the financial sector while recurrent neural network (RNN) models are successfully used in many large-scale industrial applications of Deep Learning. Our article combines these two methods in a non-trivial way and proposes a model, which we call th…
We study the estimation of the parametric components of single and multiple index volatility models. Using the first- and second-order Stein's identities, we develop methods that are applicable for the estimation of the variance index in the high-dimensional setting requiring finite moment condition, which allows for h…
AGOP from KRR recovers central subspace in fewer samples than needed for prediction.
problem Recovering low-dimensional structure in multi-index polynomial functions.
method Fit kernel ridge regression and compute AGOP from the fitted predictor.
result AGOP's top eigenspace recovers the central subspace in samples.
Neural networks learn complex functions efficiently near information-theoretic limits.
problem Understanding how neural networks learn high-dimensional features.
method Gradient descent learning of a Gaussian Multi-index model with hidden subspace.
result A standard two-layer neural network can learn the target with optimal sample and time complexity.
The paper addresses fairness in machine learning models through structural econometrics, projecting indexes into null spaces to find fair solutions.
problem Fairness concerns in machine learning, especially regarding disadvantaged groups.
method Model fairness as a linear operator, projecting indexes into null spaces to find fair solutions, balancing status quo and full fairness.
result Achieving approximate fairness by introducing a fairness penalty and balancing influences.
Paper finds significant impact of stock market swings on equity risk premium predictability.
problem Predicting equity risk premium based on stock market behavior changes.
method Introduced Bullish Index and used FDMAA for returns analysis; considered 28 indicators.
result Positive shocks in Bullish Index correlate with strong equity risk premium predictability for up to six months, while negative shocks correlate for up to nine months.
Study improves stock return prediction by switching between economic states, outperforming traditional methods.
problem Improving stock return prediction across economic regimes.
method State-switching specification using the slope of the yield curve, with an Aligned Economic Index.
result The Aligned Economic Index outperforms traditional predictors, especially during market turbulence.
A neural network estimates sampling distributions for hard problems where classical methods fail.
problem Bootstrap failure in estimating sampling distributions for specific statistics.
method Neural network trained on simulated datasets using pinball loss.
result Neural network attains 95% nominal coverage and 97% improvement over classical methods on four bootstrap-failure problems.
The C-index Multiversestat.ML
C-index varies among software, complicating model comparison.
problem Variation in C-index calculations across software.
method Comparison of C-index estimators in R and Python.
result Different implementations yield varying results.
Robust Estimation of the Tail Index of a Single Parameter Pareto Distribution from Grouped Datastat.ME
Paper introduces a new robust method for estimating Pareto tail index from grouped data.
problem Limited robust methods for estimating Pareto tail index from grouped data.
method Method of Truncated Moments (MTuM)
result Inferential justification and validation of MTuM through simulation study.
Bayesian approach for constructing and rebalancing sparse index-tracking portfolios.
problem Sparse tracking of a reference index with uncertainty quantification.
method Sparse linear regression with Laplace prior, empirical-Bayes calibration, Langevin-type MCMC, threshold-based rules.
result Posterior uncertainty on tracking error, portfolio composition, and rebalancing moves.