We investigate the impact of available information on the estimation of the default probability within a generalized structural model for credit risk. The traditional structural model where default is triggered when the value of the firm's asset falls below a constant threshold is extended by relaxing the assumption of…
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48 results for “informational threshold”
We define the information threshold in Bayesian decision-making.
problem Understanding the optimal amount of information for reliable classification.
method Defining the information threshold as the point of maximum curvature in the prior vs. posterior curve.
result At the information threshold, additional evidence does not significantly improve posterior probability.
Study on detecting and recovering hidden dense cycles in random graphs.
problem Detecting and recovering hidden dense cycles in random graphs.
method Information-theoretic analysis of thresholds for detection and recovery.
result Characterization of information-theoretic thresholds for detection and recovery.
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…
The paper sets thresholds for testing correlation in hypergraphs, distinguishing between independent and correlated states.
problem Testing correlation between two hypergraphs under different models.
method Derives sharp information-theoretic thresholds for distinguishing between null and alternative hypotheses.
result The testing threshold decreases as the hypergraph's uniformity (m) increases, making correlation testing easier for higher uniformity.
New algorithm achieves strong consistency in binary non-uniform hypergraph classification.
problem Node classification on binary non-uniform hypergraphs with varying edge probabilities.
method Proposes a refinement algorithm using power iteration on weighted adjacency matrices.
result Proves optimality of the refinement algorithm, achieving strong consistency and IT lower bound.
This paper sets thresholds for recovering vertex correspondences in partially correlated graphs.
problem Recovering hidden vertex correspondences in partially correlated graphs.
method Proposed partially correlated Erdős-Rényi graphs model; information-theoretic thresholds; correlated functional digraphs.
result Optimal rates for partial and exact recovery of vertex correspondences.
Evaluation of the marginal likelihood plays an important role in model selection problems. The widely applicable Bayesian information criterion (WBIC) and singular Bayesian information criterion (sBIC) give approximations to the log marginal likelihood, which can be applied to both regular and singular models. When the…
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.
We provide high probability finite sample complexity guarantees for hidden non-parametric structure learning of tree-shaped graphical models, whose hidden and observable nodes are discrete random variables with either finite or countable alphabets. We study a fundamental quantity called the (noisy) information threshol…
Study sharpens threshold for matching correlated graphs without labels.
problem Matching latent vertex correspondences in correlated random graphs.
method Analyzes information-theoretic limits for correct vertex matching in sub-sampled graphs.
result Establishes a sharp information-theoretic threshold for vertex matching recovery.
Paper uses SDP for community detection with side information.
problem Community detection in graphs with additional non-graph data.
method Formulates SDP relaxation for maximum likelihood node labeling with side information.
result SDP achieves same exact recovery threshold as maximum likelihood with side information.
Study community detection in multi-view data with various types of information.
problem Community detection in multi-view data with different types of information.
method Unified theoretical framework, mutual information analysis, sharp thresholds, iterative algorithms.
result Sharp thresholds for community recovery in various multi-view settings.
Azure (the cloud service provided by Microsoft) is composed of physical computing units which are called nodes. These nodes are controlled by a software component called Fabric Controller (FC), which can consider the nodes to be in one of many different states such as Ready, Unhealthy, Booting, etc. Some of these state…
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.
A new SSL method uses instance-dependent thresholds to improve accuracy.
problem Improving semi-supervised learning by better selecting confident unlabeled instances.
method Proposes instance-dependent thresholds that vary based on the ambiguity and error rates of pseudo-labels for each unlabeled instance.
result Demonstrates that instance-dependent thresholds provide a probabilistic guarantee for correct pseudo-labels.
I show the equivalence between a model of financial contagion and the threshold model of global cascades proposed by Watts (2002). The model financial network comprises banks that hold risky external assets as well as interbank assets. It is shown that a simple threshold model can replicate the size and the frequency o…
This work suggests modifications to a previously introduced class of heterogeneous agent models that allow for the inclusion of different types of agent motivations and behaviours in a unified way. The agents operate within a highly simplified environment where they are only able to be long or short one unit of the ass…
Paper introduces threshold invariant fairness to ensure equitable predictions across different groups.
problem Machine learning models can be unfair to certain groups based on sensitive attributes.
method Proposes threshold invariant fairness and uses two approximation methods to equalize risk distributions.
result Demonstrates effectiveness in alleviating threshold sensitivity in fairness models.
Sharp thresholds and contiguity for community detection in contextual SBM.
problem Community detection in graphs with high-dimensional node-covariates.
method Contextual Stochastic Block Model, non-rigorous cavity method, information theory.
result Established the sharp threshold for detection and weak recovery in the contextual SBM.
The stochastic block model (SBM) is a random graph model with different group of vertices connecting differently. It is widely employed as a canonical model to study clustering and community detection, and provides a fertile ground to study the information-theoretic and computational tradeoffs that arise in combinatori…
The stochastic block model is one of the oldest and most ubiquitous models for studying clustering and community detection. In an exciting sequence of developments, motivated by deep but non-rigorous ideas from statistical physics, Decelle et al. conjectured a sharp threshold for when community detection is possible in…
A learning-based algorithm optimizes admission control in a queuing system.
problem Optimizing admission decisions in a queuing system with unknown parameters.
method Proposes a learning-based dispatching algorithm to minimize regret compared to optimal policies.
result Achieves optimal regret bounds for different scenarios of unknown parameters.
This paper resolves the all-or-nothing phase transition in graph matching.
problem Recovering vertex correspondence between edge-correlated random graphs.
method Analysis of mutual information, truncated second-moment computation, and maximum likelihood estimator.
result Sharp thresholds for correct matching in both dense and sparse graphs.
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.
Paper bounds tensor decomposition's RLCT, aiding Bayesian inference.
problem Unclear mathematical property of tensor decomposition.
method Algebraic geometrical method for upper bound derivation.
result Upper bound of real log canonical threshold (RLCT) derived.
New model for community detection with side information improves recovery accuracy.
problem Community detection in networks with additional node data.
method Data Block Model (DBM) with Chernoff--TV divergence for threshold characterization and efficient algorithm.
result Sharp exact recovery threshold and efficient algorithm for DBM.
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.
A central problem of random matrix theory is to understand the eigenvalues of spiked random matrix models, introduced by Johnstone, in which a prominent eigenvector (or "spike") is planted into a random matrix. These distributions form natural statistical models for principal component analysis (PCA) problems throughou…
"Sparse" neural networks, in which relatively few neurons or connections are active, are common in both machine learning and neuroscience. Whereas in machine learning, "sparsity" is related to a penalty term that leads to some connecting weights becoming small or zero, in biological brains, sparsity is often created wh…
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.
Study on sparse recovery with mixed-quality data, establishing sample-size conditions.
problem Sparse recovery with heterogeneous noise from high- and low-quality sources.
method Establishes linear trade-off for sufficient conditions, analyzes LASSO algorithm.
result Linear trade-off for sufficient conditions, robustness of LASSO to data heterogeneity.
We study online learning when partial feedback information is provided following every action of the learning process, and the learner incurs switching costs for changing his actions. In this setting, the feedback information system can be represented by a graph, and previous works studied the expected regret of the le…
In this work, a classification method for SSVEP-based BCI is proposed. The classification method uses features extracted by traditional SSVEP-based BCI methods and finds optimal discrimination thresholds for each feature to classify the targets. Optimising the thresholds is formalised as a maximisation task of a perfor…
We consider the problem of Gaussian mixture clustering in the high-dimensional limit where the data consists of points in dimensions, and stays finite. Using exact but non-rigorous methods from statistical physics, we determine the critical value of and the distance between…
The study finds that memorization is necessary or harmful depending on the prior distribution and noise level.
problem The impact of memorization on generalization in overparameterized models.
method An overparameterized linear model with general priors in a Bayesian setup.
result Explicit conditions for optimal generalization based on the prior distribution and noise level.
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.
Sharp threshold for exact recovery in non-uniform hypergraph stochastic block model.
problem Community detection in random hypergraphs with non-uniform hyperedge probabilities.
method Sharp threshold established; two efficient algorithms for exact recovery.
result Sharp threshold for exact recovery; information-theoretic lower bound on misclassification.
Iterative thresholding algorithms are well-suited for high-dimensional problems in sparse recovery and compressive sensing. The performance of this class of algorithms depends heavily on the tuning of certain threshold parameters. In particular, both the final reconstruction error and the convergence rate of the algori…
Gaussian latent tree models, or more generally, Gaussian latent forest models have Fisher-information matrices that become singular along interesting submodels, namely, models that correspond to subforests. For these singularities, we compute the real log-canonical thresholds (also known as stochastic complexities or l…
Study proposes an active subsampling method for estimating individualized thresholds in high-dimensional data.
problem Estimating optimal individualized thresholds in high-dimensional data with limited labeled samples.
method Developed a K-step active subsampling algorithm to iteratively select and label the most informative data points.
result Revealed a phase transition phenomenon in the estimation of with respect to the smoothness of the conditional density.
Noisy Max and Sparse Vector are selection algorithms for differential privacy and serve as building blocks for more complex algorithms. In this paper we show that both algorithms can release additional information for free (i.e., at no additional privacy cost). Noisy Max is used to return the approximate maximizer amon…
Stop-loss rules are often studied in the financial literature, but the stop-loss levels are seldom constructed systematically. In many papers, and indeed in practice as well, the level of the stops is too often set arbitrarily. Guided by the overarching goal in finance to maximize expected returns given available infor…
The tree reconstruction problem is to collect and analyze massive data at the th level of the tree, to identify whether there is non-vanishing information of the root, as goes to infinity. Its connection to the clustering problem in the setting of the stochastic block model, which has wide applications in machin…
The study analyzes when Bayesian averaging over decision trees is reliable.
problem When do Bayesian model averaging weights over decision trees provide reliable information?
method Closed-form solution for Bayesian decision trees with Catalan-exponential priors.
result Established a complete non-asymptotic theory of rational commitment thresholds.
In this paper, we introduce a new online decision making paradigm that we call Thresholding Graph Bandits. The main goal is to efficiently identify a subset of arms in a multi-armed bandit problem whose means are above a specified threshold. While traditionally in such problems, the arms are assumed to be independent, …
A central problem of random matrix theory is to understand the eigenvalues of spiked random matrix models, in which a prominent eigenvector is planted into a random matrix. These distributions form natural statistical models for principal component analysis (PCA) problems throughout the sciences. Baik, Ben Arous and Pé…
Statistical-computational gap found in aligning multiple Gaussian graphs.
problem Aligning multiple Gaussian graphs with unknown signals.
method Generalized informational threshold and computational barrier analysis.
result Existence of a statistical-computational gap in multiple Gaussian graph alignment.