Dynamic tracking error framework shows similar performance but varying volatility across different constraints.
problem Differences in governance parameters between Total Portfolio Approach and Strategic Asset Allocation.
method Portfolio simulations using U.S. equity and bond data from 2000 to 2026, spanning 2004 to 2026.
result Realized tracking error volatility varies 12-fold across different constraints, with costs highest during crises.
New approach uses Gaussian processes to learn and track complex systems with guaranteed accuracy.
problem Inaccurate first principle models for complex systems due to data complexity.
method Bayesian prediction error bound for Gaussian process regression, derived from kernel-based data density.
result Achieves vanishing tracking error with increasing data density, providing time-varying accuracy guarantees.
High-probability bound for distributed stochastic approximation tracking error.
problem Analyzing the convergence of distributed stochastic approximation schemes.
method Analysis using ODE approach to stochastic approximation.
result High probability bound for tracking error between iterates and limiting differential equation.
Study efficient rebalancing strategies for portfolio tracking error.
problem Optimizing portfolio rebalancing under high-frequency asset price models.
method Discrete-time rebalancing strategies derived from continuous model.
result Asymptotically efficient sequence of simple strategies.
This paper optimizes portfolio selection by penalizing tracking error, improving Sharpe ratio.
problem Optimizing portfolio allocation with a penalty for deviation from a reference portfolio.
method Formulated as a McKean-Vlasov control problem, provides explicit solutions and asymptotic expansions.
result The penalized portfolio strategy outperforms standard mean-variance and reference portfolios in most cases.
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.
The efficiency of a modern economy depends on what we call the Value-Tracking Hypothesis: that market prices of key assets broadly track some underlying value. This can be expected if a sufficient weight of market participants are valuation-based traders, buying and selling an asset when its price is, respectively, bel…
New RL method improves financial index tracking accuracy.
problem Optimizing financial index tracking with dynamic market information.
method Discrete-time dynamic model, Banach fixed point iteration, deep reinforcement learning.
result Proposed RL method outperforms benchmarks in tracking accuracy.
Passive investing can incur hidden costs due to market timing inefficiencies.
problem Hidden costs in passive investing due to market timing inefficiencies.
method Analysis of passive investing strategies, including gradual share acquisition and post-announcement trading.
result Post-announcement trading can earn significant profits, often exceeding 1%.
The paper analyzes constrained optimal portfolios in high dimensions using novel statistical learning techniques.
problem Forming optimal portfolios with constraints in high-dimensional asset spaces.
method CROWN method integrating factor models with nodewise regression for estimation in large dimensions.
result Demonstrates estimation consistency and convergence rates for constrained portfolio weights, risk, and Sharpe Ratio.
Perfect tracking control for real-world Euler-Lagrange systems is challenging due to uncertainties in the system model and external disturbances. The magnitude of the tracking error can be reduced either by increasing the feedback gains or improving the model of the system. The latter is clearly preferable as it allows…
Paper solves tracking control for (x,u)-flat systems using classical states.
problem Tracking control for (x,u)-flat systems. method Quasi-static feedback of classical states.
result Achieves linear, decoupled and asymptotically stable tracking error dynamics.
Partial (replication) index tracking is a popular passive investment strategy. It aims to replicate the performance of a given index by constructing a tracking portfolio which contains some constituents of the index. The tracking error optimisation is quadratic and NP-hard when taking the L0 constraint into account so …
Index tracking is a popular form of asset management. Typically, a quadratic function is used to define the tracking error of a portfolio and the look back approach is applied to solve the index tracking problem. We argue that a forward looking approach is more suitable, whereby the tracking error is expressed as expec…
This paper identifies and analyzes biases in risk-adjusted index weighting methods, affecting social welfare and market fairness.
problem Biases in risk-adjusted index weighting methods lead to tracking errors and fraud in indices and ETFs.
method Characterizes and analyzes the biases and adverse effects of risk-adjusted index weighting methods.
result These biases reduce social welfare and can enable harmful arbitrage activities.
Two novel procedures track quantiles efficiently using an oracle.
problem Setting step size and tuning parameters for incremental quantile estimators.
method Estimate MSE, decompose into variance and bias, use oracle to select best estimator.
result Efficient quantile tracking with error close to theoretical optimum.
DD algorithm tracks test error from train error without validation data.
problem Systematic generalization gap between train and test errors in modern model training.
method Decoupled descent (DD) algorithm that cancels data reuse biases via approximate message passing.
result DD algorithm rigorously demonstrates zero-cost validation and 100% data utilization.
A spiral unibike track emerges from a mathematical construction.
problem Finding a unibike curve with a spiral shape.
method Starting with a polar square root curve, iteratively applying a differential equation to create a spiral unibike track.
result A spiral unibike curve is found with a precision error less than 10^-7.
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).
Paper introduces EnDKF for more accurate pose tracking.
problem Accurate pose tracking with directional uncertainty.
method EnDKF integrates unit-quaternion attitude representation for better directional uncertainty capture.
result Significant reduction in error compared to traditional methods.
Optimizes sliding window approach for tracking Gaussian densities.
problem Improving tracking performance of Gaussian density estimation.
method Theoretical analysis of sliding window Gaussian Kernel Density Estimators.
result Empirical evidence shows improved tracking performance with optimal weight sequence.
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.
Online Multi-Object Tracking (MOT) from videos is a challenging computer vision task which has been extensively studied for decades. Most of the existing MOT algorithms are based on the Tracking-by-Detection (TBD) paradigm combined with popular machine learning approaches which largely reduce the human effort to tune a…
This paper reviews and analyzes various modeling approaches for financial index tracking.
problem Efficient replication of market index performance in financial markets.
method Categorization into three frameworks: optimization, statistical, and machine learning; empirical study on S&P 500 dataset.
result Optimization-based models deliver the most precise index tracking, statistical-based models achieve the strongest return-risk balance, and data-driven models provide competitive performance.
The paper analyzes Adam and SGD in nonstationary optimization, revealing tradeoffs between noise and drift.
problem Analyzing Adam and SGD in nonstationary optimization problems.
method Theoretical analysis of Adam and SGD under non-stationary stochastic objectives, separating two regimes.
result Characterizes the tradeoff between noise and drift in Adam and SGD, revealing when adaptive step-sizing is beneficial or harmful.
Method improves volatility targeting for index construction.
problem High turnover, leverage spikes, and sensitivity to estimation error in existing volatility-targeting strategies.
method Proportional-control approach for setting index weights that corrects tracking error through feedback.
result The proportional-control approach achieves the target volatility more effectively than open-loop alternatives.
Deep learning predicts market sensitivities for cost-effective index tracking.
problem Costly and impractical replication of index funds.
method Learning to predict market sensitivities using deep learning models.
result Significant reduction in prediction errors compared to historical methods.
SOOTT framework optimizes target tracking with robust and learning-augmented algorithms.
problem Optimizing target tracking in dynamic environments with adversarial perturbations.
method Integrates robust and learning-augmented algorithms for online decision-making.
result CoRT learning-augmented algorithm strictly improves over robust BEST when predictions are accurate.
We study involuntary micro-movements of the eye for biometric identification. While prior studies extract lower-frequency macro-movements from the output of video-based eye-tracking systems and engineer explicit features of these macro-movements, we develop a deep convolutional architecture that processes the raw eye-t…
From human crowds to cells in tissue, the detection and efficient tracking of multiple objects in dense configurations is an important and unsolved problem. In the past, limitations of image analysis have restricted studies of dense groups to tracking a single or subset of marked individuals, or to coarse-grained group…
A deep learning model improves pedestrian tracking accuracy.
problem Pedestrian tracking accuracy is low, especially with inertial measurement unit.
method Deep learning model using IMU and LIDAR data, attention mechanism.
result Preliminary results show improved accuracy.
Momentum SGD fails to track nonstationary optima due to drift amplification.
problem Tracking nonstationary optima in stochastic optimization.
method Theoretical analysis of SGD and momentum variants under strong convexity and smoothness.
result Momentum incurs a drift-amplification penalty that diverges as the momentum parameter approaches 1, leading to systematic lag.
This study models target trajectories using stochastic processes for efficient tracking.
problem Efficiently modeling and predicting target trajectories in continuous time.
method Decomposes trajectory modeling into deterministic and stochastic components using Gaussian or Student's-t processes. result Demonstrates superior performance in tracking maneuvering targets compared to existing methods.
Commodity exchange-traded funds (ETFs) are a significant part of the rapidly growing ETF market. They have become popular in recent years as they provide investors access to a great variety of commodities, ranging from precious metals to building materials, and from oil and gas to agricultural products. In this article…
Neural network Kalman filtering improves 3D ultrasound object tracking.
problem Accurate and robust 3D positional estimation from 2D ultrasound data.
method Neural network training for out-of-plane offset estimation, combined with Kalman filtering.
result Mean error of 0.1mm for simulated data, 0.2mm for experimental data.
In microsurgery, lasers have emerged as precise tools for bone ablation. A challenge is automatic control of laser bone ablation with 4D optical coherence tomography (OCT). OCT as high resolution imaging modality provides volumetric images of tissue and foresees information of bone position and orientation (pose) as we…
Recurrent neural networks' hidden state can be reconstructed from its past, providing a theoretical framework for stability and tracking.
problem Hidden-state stability in RNNs
method Backward coherence analysis
result Almost-sure convergence, rates under mixing, interpretable limiting representation, finite pathwise stopping times, and theoretical framework for time-uniform confidence sequences.
We study the tracking of a trajectory for a nonholonomic system by recasting the problem as a constrained optimal control problem. The cost function is chosen to minimize the error in positions and velocities between the trajectory of a nonholonomic system and the desired reference trajectory, both evolving on the dist…
Bayesian deep learning improves seismic imaging uncertainty.
problem Uncertainty in seismic imaging due to data noise and linearization errors.
method Combines Bayesian inference and deep neural networks to quantify uncertainty in horizon tracking.
result Uncertainty in automatically tracked horizons can be quantified and visualized.
The paper provides guarantees for feedback control with sensor errors.
problem Certifying performance and safety in feedback control systems with sensor errors.
method Solving a supervised learning problem to characterize sensor errors and providing uniform error bounds.
result Finite-time convergence rate on sub-optimality of using a regressor in closed-loop for waypoint tracking.
We analyze the errors arising from discrete readjustment of the hedging portfolio when hedging options in exponential Levy models, and establish the rate at which the expected squared error goes to zero when the readjustment frequency increases. We compare the quadratic hedging strategy with the common market practice …
Improved stochastic approximation method reduces residual error.
problem Reducing residual error in stochastic approximation algorithms.
method Fixed-schedule one-quarter barrier and bias-corrected acceleration.
result Achieves T−1/2+o(1) residual reduction with O(1) primitive samples. Study best arm identification with limited precision sampling in bandits.
problem Limited precision sampling in multi-armed bandit problems.
method Proposed a modified tracking-based algorithm to handle non-unique optimal allocations and presented non-asymptotic bounds.
result Asymptotically optimal tracking-based algorithm for best arm identification.
New method tracks time-varying parameters in data.
problem Tracking unknown time-varying parameters in data.
method Stochastic gradient descent-based recursive scheme with log-likelihood as gain function.
result Convergence in mean-square error in a suitable neighborhood of the unknown parameter.
Gradient filters track moving parameters under noisy data and misspecification.
problem Tracking multidimensional time-varying parameters under noisy observations and model misspecification.
method Gradient-based filters update parameters using the gradient of a postulated objective function, evaluated at either the predicted or updated parameters.
result Novel sufficient conditions for exponential stability of the filtered parameter path, and finite-sample and asymptotic mean squared error bounds.
A new method tracks market performance without active management.
problem Active portfolio management does not outperform benchmarks.
method Developed a hybrid PCA-based tracking portfolio strategy.
result The hybrid PCA strategy outperforms optimization-based approaches.
We present a novel spectral learning algorithm for simultaneous localization and mapping (SLAM) from range data with known correspondences. This algorithm is an instance of a general spectral system identification framework, from which it inherits several desirable properties, including statistical consistency and no l…
Paper introduces MoTEF for faster decentralized optimization with compressed communication.
problem Efficiency bottleneck in decentralized machine learning applications.
method Integrates communication compression with Momentum Tracking and Error Feedback.
result Significantly outperforms existing methods under arbitrary data heterogeneity.