Modeling firm default with a variable threshold based on management decisions.
problem Estimating default probability with asymmetric information.
method Generalized structural model with a variable default threshold.
result The information level significantly impacts default probability and credit yield spread.
Study derives algorithmic detectability threshold for stochastic block model with EM and BP.
problem Detectability of stochastic block model in practice when parameters are unknown.
method Used expectation-maximization (EM) algorithm with belief propagation (BP).
result Algorithmic detectability threshold differs from Nishimori condition.
Paper proposes a method to identify optimal threshold for stock market networks.
problem Challenges in identifying the optimal threshold for reliable stock network construction.
method Dynamic consistence between threshold network and stock market, optimal threshold maximized by consistence function.
result Optimal threshold value of 0.28 for stocks in S&P 500 Index.
Optimal rates for learning hidden tree structures are determined.
problem Learning hidden tree structures from noisy data.
method Study of the (noisy) information threshold and the Chow-Liu algorithm.
result Optimal rates for structure recovery are inversely proportional to the information threshold squared.
New method simplifies Graphical Lasso for chordal graphs.
problem Sparse covariance estimation for large graphs.
method Closed-form solution for chordal graphs, reducing GL to matrix completion.
result Graphical Lasso and thresholding equivalence holds for chordal structures.
A RL algorithm learns optimal multi-threshold policies for MDPs.
problem Overcoming the curse of dimensionality in MDPs.
method Structure-aware RL algorithm exploiting multi-threshold optimal policies.
result The algorithm converges to the optimal policy asymptotically.
Investigates probability of error in structured thresholding bandit problems.
problem Probability of misclassifying arms in structured thresholding bandit problems.
method Analyzes two shape constraints: monotonic increasing and concave sequences of arm means.
result Upper and lower bounds for the probability of error match up to constants in the problem dependent regime.
Based on the daily data of American and Chinese stock markets, the dynamic behavior of a financial network with static and dynamic thresholds is investigated. Compared with the static threshold, the dynamic threshold suppresses the large fluctuation induced by the cross-correlation of individual stock prices, and leads…
GrAPL identifies arms above a threshold using graph similarity.
problem Efficiently identifying arms with means above a threshold in a graph-structured bandit problem.
method Thresholding Graph Bandits with GrAPL algorithm exploiting graph structure and reward homophily.
result GrAPL effectively identifies arms above a threshold using graph structure and reward homophily.
Polynomial neural networks explore thresholds for maximum expressiveness.
problem Understanding the limits of polynomial neural networks' expressiveness.
method Introducing activation degree threshold to measure network expressiveness and proving its existence and upper bounds.
result Polynomial neural networks with equi-width architectures achieve the maximum expressiveness.
This work interprets GELU and related activations via a first-order loss function.
problem Understanding and optimizing activation functions in neural networks.
method Complementary interpretation using the Gaussian first-order loss function.
result Calibrated or learned uniform-threshold gates are competitive and often outperform GELU, ReLU, and SiLU/Swish.
New RL algorithm learns optimal policies for MDPs using known structure.
problem Overcoming curse of dimensionality and modeling in MDPs.
method Structure-aware online learning algorithm exploiting known threshold policy.
result Proposed algorithm converges to optimal policy with significant speed improvements.
Graphical Lasso and thresholding methods are shown to be equivalent under certain conditions, leading to closed-form solutions.
problem Learning the structure of undirected graphical models.
method Comparison of Graphical Lasso and thresholding methods, development of sign-consistent and inverse-consistent matrices, and derivation of closed-form solutions.
result Graphical Lasso and thresholding methods are equivalent under specific conditions, leading to closed-form solutions.
New method identifies extreme risk propagation in financial networks.
problem Understanding extreme risk in financial networks.
method Max-linear structural equation model, hard-thresholding, Hamming distance.
result Sparse DAG for extreme risk propagation estimated.
We study graph matching with correlated Gaussian features and find thresholds for exact recovery.
problem Graph matching with correlated Gaussian features.
method Information-theoretic thresholds and conditions for exact and almost exact recovery.
result Contextual information introduces a richer structure, with thresholds for exact and almost exact recovery no longer coinciding.
Unfolded ISTA achieves linear convergence for sparse signal recovery.
problem Understanding and improving convergence of iterative algorithms in sparse signal recovery.
method Introducing weight structure and incorporating thresholding in the network.
result Unfolded ISTA can achieve linear convergence, better than sublinear convergence of ISTA/FISTA.
New algorithms detect communities in sparse graphs with labeled data.
problem Detecting communities in sparse graphs with limited labeled data.
method Introduces two algorithms: combinatorial and optimization-based, to integrate labeled data with graph structures.
result Detection of communities is feasible throughout the parameter domain with arbitrary labeled data.
Study examines financial market structure changes during the COVID-19 crash using a novel MI approach.
problem Analyzing nonlinear dependencies among major stocks during market crashes.
method Conditional p-threshold mutual information (MI) and Minimum Spanning Tree (MST) framework.
result Financial networks become more integrated during crashes, with increased periphery vulnerability.
STAT-SVD method reduces high-dimensional data sparsity, achieving optimal estimation.
problem Sparse tensor singular value decomposition for high-dimensional data.
method STAT-SVD method with double projection & thresholding scheme.
result STAT-SVD provides sharp thresholding criterion and minimax rate-optimal estimation.
AIHT improves online high-dimensional quantile regression by separating support discovery and refinement.
problem Online high-dimensional quantile regression with structural sparsity.
method Adaptive Iterative Hard Thresholding (AIHT) alternates stochastic updates with adaptive hard-thresholding steps.
result AIHT achieves logarithmic regret for the sliding-window objective in high-dimensional settings.
This study optimizes multi-modal learning thresholds and algorithms in high dimensions.
problem Optimizing multi-modal learning performance in high-dimensional data.
method Analytical quantification and derivation of AMP algorithm with state evolution analysis.
result Bayes-optimal performance and recovery thresholds derived for multi-modal data.
Paper studies community detection in censored hypergraphs using information theory.
problem Community detection in censored hypergraphs with missing values.
method Information-theoretic approach, polynomial-time algorithm, spectral algorithm with refinement.
result Derives information-theoretic threshold for exact recovery of community structure.
STR reparameterizes DNN weights with soft thresholds for better sparsity and accuracy.
problem Improving sparsity in DNNs for better accuracy and lower inference cost.
method Soft Threshold Reparameterization (STR) using the soft-threshold operator on DNN weights.
result STR achieves state-of-the-art accuracy and reduces FLOPs by up to 50%.
Optimal policy found for observing noisy time series.
problem Minimizing posterior variance plus observation costs in discrete-time Gaussian random walks.
method Developed a simple threshold-based policy and proved its optimality.
result Simple threshold policy is optimal for observing noisy time series.
Study examines stock market connections before, during, and after the 2008 financial crisis.
problem Effects of the 2008 global financial crisis on stock market connectivity.
method Generated complex networks from cross-correlation matrices, using threshold networks and minimal spanning trees.
result During the crisis, countries in different zones had varying levels of connectivity.
We study the pricing of credit derivatives with asymmetric information. The managers have complete information on the value process of the firm and on the default threshold, while the investors on the market have only partial observations, especially about the default threshold. Different information structures are dis…
Automatically tunes parameters of rule-based systems using labeled data.
problem Tuning parameters of complex rule-based systems efficiently.
method Structured differential learning for approximate gradient descent.
result Successfully adjusts system values for over 100 parameters.
We study the fundamental limits on learning latent community structure in dynamic networks. Specifically, we study dynamic stochastic block models where nodes change their community membership over time, but where edges are generated independently at each time step. In this setting (which is a special case of several e…
New findings on community recovery in SBM with many communities.
problem Determining community recovery conditions in SBM with more than sqrt(n) communities.
method Constructing motifs and counting them to prove community recovery above the proposed threshold.
result Proving community recovery above the proposed threshold in SBM with K >= sqrt(n) communities.
We consider the effects of the global financial crisis through a local Korean financial market around the 2008 crisis. We analyze 185 individual stock prices belonging to the KOSPI (Korea Composite Stock Price Index), cosidering three time periods: the time before, during, and after the crisis. The complex networks gen…
Optimal iterative thresholding algorithms improve upon hard and soft thresholding.
problem Optimizing sparsity or rank constraints in optimization problems.
method Developed the notion of relative concavity for thresholding operators, finding a new class of operators that are optimal.
result A new class of thresholding operators, including ℓq thresholding and reciprocal thresholding, achieves the strongest convergence guarantee. Algorithm recovers components from few samples of high-dimensional vectors with structured sparsity.
problem Demixing high-dimensional vectors from few samples with structured sparsity.
method Iterative thresholding algorithm for stable component recovery.
result Algorithm provably recovers components with n=O(s) samples, achieving fast convergence and per-iteration complexity. Paper develops new methods for binary classification with complex performance measures.
problem Complex performance measures in binary classification are not decomposable and require new theoretical and methodological developments.
method Identifies Karmic and threshold-quasi-concavity properties, and develops a computationally practical plug-in classifier.
result Bayes optimal classifier is a threshold function of conditional probability, leading to practical classification error analysis.
We study two global structural properties of a graph Γ, denoted AS and CFS, which arise in a natural way from geometric group theory. We study these properties in the Erdös--Rényi random graph model G(n,p), proving a sharp threshold for a random graph to have the AS property asymptotically almost surely, and giving f…
The study examines when to trust confidence thresholding in pseudo-labelling regression.
problem Calibrated probabilities from classifiers used for pseudo-labelling need careful handling to avoid bias in downstream regression.
method Developed a diagnostic apparatus to predict and bound the bias induced by confidence thresholding, derived a closed-form expression for the attenuation bias.
result The bias can be predicted from the residual score variance V∗, motivating a structural separation between classifier features and downstream controls. Critical volatility triggers log-normal to power-law transitions in interconnected systems.
problem Understanding the transition from log-normal to power-law distributions in interconnected systems.
method Analyzing an infinite option-on-option chain model, deriving a critical volatility threshold.
result A critical volatility threshold of approximately 250.66% for unconditional cases, dropping to 125.3% with selective survival.
Solves asset allocation for investors with utility functions and limits.
problem Investor risk and utility with position limits.
method Analytical solution for piecewise-linear utility function with position limits.
result Simple functional form representing risk cost.
Optimal control of reserve assets for stablecoins to maintain peg stability.
problem Balancing immediate liquidity and yield on reserve assets for stablecoin peg maintenance.
method Developed a stochastic model predictive control framework with moment closure for event intensities, incorporating a soft-thresholding structure for rebalancing.
result Optimal policy shifts predictably toward cash as expected outflows intensify or windows lengthen, preserving most bill carry in calm markets and quickly building cash during stress.
Developed a new thresholding method that connects soft and hard thresholding.
problem Connecting soft and hard thresholding methods in data analysis.
method Scaled soft thresholding method with empirical scaling values.
result Found two sources of over-fitting in the scaled soft thresholding method.
Develops RES metrics for stable rare-event forecasting evaluation.
problem Challenges in evaluating forecasts of rare events.
method Rare-event-stable (RES) metrics designed to maintain stable thresholds under extreme rarity.
result RES metrics maintain stable thresholds, consistent model rankings, and near-complete prevalence invariance.
IHT improves sparse distribution learning.
problem Learning sparse discrete distributions.
method Iterative hard thresholding as a solution, with a greedy approximate projection.
result IHT achieves state of the art results for sparse distribution learning.
Contagion maps detect network structure in noisy data.
problem Detecting underlying manifold structure in noisy data.
method Using activation times in threshold contagions to map network nodes to high-dimensional space.
result Contagion maps reliably detect manifold structure in noisy data, while Isomap fails.
Guarantees sparse recovery for neural networks with iterative hard thresholding.
problem Recovering sparse network weights in neural networks.
method Structural properties of sparse network weights and iterative hard thresholding algorithm.
result Simple iterative hard thresholding algorithm recovers sparse network weights exactly using linear memory.
Undirected graphs are often used to describe high dimensional distributions. Under sparsity conditions, the graph can be estimated using ℓ1-penalization methods. We propose and study the following method. We combine a multiple regression approach with ideas of thresholding and refitting: first we infer a sparse u…
MLShrink integrates machine learning with wavelet shrinkage for denoising.
problem Denoising signals with uncertain magnitudes
method Combines wavelet shrinkage with machine learning
result Preserves simplicity for signal coefficients while allowing data-adaptive decisions for ambiguous coefficients
New method learns sparse distributions by thresholding samples, improving performance and efficiency.
problem Sparse coding optimization in high-dimensional problems is computationally expensive and inefficient.
method Proposes a new variational sparse coding approach that learns sparse distributions by thresholding samples.
result Shows superior performance, statistical efficiency, and gradient estimation compared to other sparse distributions.
New insights into binary perceptron reveal phase transitions and algorithmic thresholds.
problem Understanding the statistical-computational gap in binary perceptron models.
method Application of fully lifted random duality theory (fl RDT) to uncover structural changes.
result Numerical estimates of constraint density thresholds align with theoretical predictions.
New model improves community detection in networks with strong assortativity.
problem Classic SBMs fail to recover assortative communities in networks with reduced information.
method Introduced a constrained SBM with strong assortativity constraints and efficient algorithms.
result Significant boost in community recovery capabilities, especially close to information-theoretic threshold.