A study on the depth of graph neural networks on sparse graphs, revealing a dichotomy based on the Kesten-Stigum ratio.
problem Determining the optimal depth of graph neural networks for sparse graphs.
method Analyzing the sparse contextual stochastic block model with a message-passing classifier.
result The value of depth is governed by the Kesten-Stigum ratio, with thresholds dividing performance into geometric and branching processes.
New algorithm detects communities even with corrupted data, reaching Kesten-Stigum threshold.
problem Robust community detection in stochastic block model with node corruptions.
method Polynomial-time algorithm using Grothendieck norm of principal submatrices.
result First algorithm to achieve weak recovery at Kesten-Stigum threshold with node corruptions.
Community detection is considered for a stochastic block model graph of n vertices, with K vertices in the planted community, edge probability p for pairs of vertices both in the community, and edge probability q for other pairs of vertices. The main focus of the paper is on weak recovery of the community based on the …
New method detects communities in complex hypergraphs, matching theoretical limits.
problem Detecting communities in non-uniform hypergraphs with varying hyperedge sizes.
method Developed a spectral theory for weighted non-backtracking operators on non-uniform hypergraphs.
result Achieved the Kesten-Stigum bound for weak recovery in a general class of non-uniform HSBMs.
Adversarial inference on tree models is possible with limited corruption, improving on Kesten-Stigum threshold.
problem Posterior inference on tree-structured graphical models in the presence of adversarial corruption.
method Dynamic programming via belief propagation, constrained adversarial corruption.
result Belief propagation can perform accurate inference with limited adversarial corruption.
New Bethe-Hessian method improves community detection in sparse networks.
problem Detect communities in sparse networks efficiently.
method Spectral clustering using the Bethe-Hessian matrix.
result Bethe-Hessian consistently estimates block number above Kesten-Stigum threshold.
Spectral method detects communities in sparse hypergraphs, achieving detection threshold.
problem Community detection in sparse hypergraphs.
method Non-backtracking operator and spectral approach.
result Spectral method achieves detection threshold for sparse HSBMs.
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.
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.
The analysis of Belief Propagation and other algorithms for the {\em reconstruction problem} plays a key role in the analysis of community detection in inference on graphs, phylogenetic reconstruction in bioinformatics, and the cavity method in statistical physics. We prove a conjecture of Evans, Kenyon, Peres, and Sch…
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…
We propose an efficient meta-algorithm for Bayesian estimation problems that is based on low-degree polynomials, semidefinite programming, and tensor decomposition. The algorithm is inspired by recent lower bound constructions for sum-of-squares and related to the method of moments. Our focus is on sample complexity bo…
We discuss - in what is intended to be a pedagogical fashion - generalized "mean-to-risk" ratios for portfolio optimization. The Sharpe ratio is only one example of such generalized "mean-to-risk" ratios. Another example is what we term the Fano ratio (which, unlike the Sharpe ratio, is independent of the time horizon)…
FORE evaluates occupancy ratios without requiring Bellman completeness.
problem Offline reinforcement learning occupancy ratio estimation.
method Fitted occupancy-ratio evaluation (FORE) using adjoint Bellman recursion.
result FORE achieves convergence in KL without Bellman completeness.
Optimal option portfolios under Sharpe Ratio maximization with skew-elliptical t-distributed returns
problem Optimal option portfolios under Sharpe Ratio maximization
method Formulation for explicit portfolio weights
result Different optimal portfolios for Sharpe Ratio and return-to-Value-at-Risk (VaR) ratio
Omega ratio, defined as the probability-weighted ratio of gains over losses at a given level of expected return, has been advocated as a better performance indicator compared to Sharpe and Sortino ratio as it depends on the full return distribution and hence encapsulates all information about risk and return. We comput…
We present a new methodology of computing incremental contribution for performance ratios for portfolio like Sharpe, Treynor, Calmar or Sterling ratios. Using Euler's homogeneous function theorem, we are able to decompose these performance ratios as a linear combination of individual modified performance ratios. This a…
The paper proposes an asset allocation strategy using the Sortino ratio for better performance.
problem Traditional asset allocation methods like the Sharpe ratio do not penalize negative returns adequately.
method The Sortino ratio is used to maximize asset allocation, penalizing only negative return variances.
result The Sortino ratio-based strategy outperforms traditional methods like the Kelly criterion.
A new ratio, the Hansen ratio, simplifies mean-variance portfolio theory.
problem Simplifying mean-variance portfolio theory.
method Introducing the Hansen ratio and extending mean-variance theory.
result The Hansen ratio provides a parsimonious description of the mean-variance efficient frontier.
Develops a new density ratio estimator for causal inference.
problem Estimation of density ratio functions in statistics.
method Super learning approach with a novel loss function.
result Empirical validation of the density ratio super learner's performance.
New PU ratio predicts long-term Bitcoin returns better than other methods.
problem Lack of convincing proxies for cryptocurrency fundamentals.
method Developed a new market-to-fundamental ratio (PU ratio) using blockchain accounting methods.
result PU ratio effectively predicts long-term Bitcoin returns compared to alternative methods.
The paper studies curves of constant-ratio in pseudo-Galilean space.
problem Characterizing curves of constant-ratio in pseudo-Galilean space.
method Analyzing spacelike curves with constant-ratio in terms of curvature functions.
result Characterization of special curves of constant-ratio in pseudo-Galilean space.
Unified framework for OOD detection using class ratio estimation.
problem Density-based OOD detection is unreliable for OOD images.
method Unified framework that builds energy-based models and employs differing base distributions, directly estimating the density ratio through class ratio estimation.
result Competitive results on OOD image problems compared to recent work.
Paper shows how to embed Möbius bands with many twists and small aspect ratios.
problem Finding the smallest aspect ratio for Möbius bands with many twists.
method Constructs a folded paper ribbon knot to bound the aspect ratio.
result Paper Möbius bands and annuli with any number of half-twists can be embedded with aspect ratio less than 8.
Direct neural ratio estimator for likelihood-free inference.
problem Efficient likelihood estimation for complex models.
method Amortized likelihood ratio estimation using neural networks.
result DNRE often outperforms previous ratio estimators.
Neural networks approximate likelihood ratios for complex models.
problem Difficulty in computing likelihood ratios for modern models.
method Applying the likelihood ratio trick with neural network classifiers.
result Different neural network setups can approximate likelihood ratios with varying performance.
Paper tackles unbounded density ratio estimation for covariate shift adaptation.
problem Understudied challenge in statistical learning: unbounded density ratios.
method Three-step estimation method: relative density ratio, truncation, and transformation.
result Established rigorous convergence guarantees for density ratio and regression estimators.
Calculates twist in Teichmüller space using cross ratios.
problem Calculating the Fenchel-Nielsen twist in Teichmüller space.
method Using cross ratio coordinates.
result Compact calculation of twist in Teichmüller space.
Study shows robust method for estimating density ratios even with heavy contamination.
problem Estimating density ratios in the presence of heavy contamination.
method Weighted density ratio estimation (DRE) with doubly strong robustness.
result Weighted DRE achieves sparse consistency under heavy contamination.
Meta-learning improves relative density-ratio estimation from limited data.
problem Estimating relative density-ratios from few instances.
method Meta-learning using neural networks to extract and embed dataset information for relative DRE.
result Meta-learning enables efficient and effective adaptation to few instances for relative DRE.
TRE improves density-ratio estimation for highly dissimilar densities.
problem Density-ratio estimation fails for significantly different densities.
method Telescoping density-ratio estimation (TRE) framework.
result TRE yields substantial improvements over existing methods for mutual information estimation.
New method resolves density ratio estimation saturation issues.
problem Error saturation in density ratio estimation methods.
method Iterated regularization to improve kernel methods.
result Achieves fast error rates on regular learning problems.
The paper describes a method to infer the signal-to-noise ratio in portfolio optimization.
problem Estimating the signal-to-noise ratio in portfolio optimization problems.
method A statistic similar to the Sharpe Ratio Information Criterion is used for inference.
result The method works well for reasonable sample and asset universe sizes.
Post hoc test for Sharpe ratio improves pairwise comparisons.
problem Improving pairwise comparisons of Sharpe ratios.
method Analogous to Tukey's test, applied after rejecting equal Signal-Noise ratios.
result Maintains nominal type I rate and is moderately powerful.
Sharpe ratio (sometimes also referred to as information ratio) is widely used in asset management to compare and benchmark funds and asset managers. It computes the ratio of the (excess) net return over the strategy standard deviation. However, the elements to compute the Sharpe ratio, namely, the expected returns and …
Paper develops estimators for unbounded density ratios with applications in error control.
problem Estimating density ratios with unbounded domains and ranges.
method Least squares and logistic regression loss functions for density ratio estimation.
result Established upper bounds on estimation errors with optimal rates for unbounded density ratios.
Estimates for plate eigenvalues with nonzero Poisson's ratio.
problem Estimating eigenvalues of a free plate with nonzero Poisson's ratio.
method Using Fourier transform to derive estimates.
result Kroger-type estimates for sums of eigenvalues.
The paper analyzes the Rashomon ratio for infinite classifier families and shows its importance for choosing good classifiers.
problem Analyzing the Rashomon ratio for infinite classifier families.
method Quantifying the Rashomon ratio in two examples and providing guarantees for estimating it.
result A large Rashomon ratio guarantees choosing a classifier with good empirical accuracy will not significantly increase empirical loss.
The estimate of a Multiperiod probability of default applied to residential mortgages can be obtained using the mean of the observed default, so called the Mean of ratios estimator, or aggregating the default and the issued mortgages and computing the ratio of their sum, that is the Ratio of means. This work studies th…
Study on Leverage Ratio in European banks during financial crises.
problem Impact of financial crises on European banks' Leverage Ratio.
method Empirical analysis using regression techniques.
result Leverage Ratio is significantly influenced by financial scenarios.
New Finsler metric on sphere disproves systolic ratio conjecture.
problem Proving the maximal systolic ratio on 2-sphere.
method Inspired by Cossarini-Sabourau, constructs a Finsler metric.
result Systolic ratio of new Finsler metric is 4π/3. Featurization improves density ratio estimation for complex data.
problem Difficulty in estimating density ratios for high-dimensional, different distributions.
method Invertible generative model to map distributions into a common feature space.
result Improved accuracy in density ratio estimation through feature space.
We generalize the natural cross ratio on the ideal boundary of a rank one symmetric spaces, or even CAT(−1) space, to higher rank symmetric spaces and (non-locally compact) Euclidean buildings - we obtain vector valued cross ratios defined on simplices of the building at infinity. We show several properties …
Smooth minimizers found for Willmore energy surfaces.
problem Finding minimizers for Willmore energy surfaces.
method Existence and smoothness established through axially symmetric surfaces with prescribed isoperimetric ratio.
result Existence and smoothness of minimizers proven.
Infinite hyperbolic manifolds share same perimeter-to-volume ratio.
problem Finding hyperbolic manifolds with a fixed perimeter-to-volume ratio.
method Constructing infinitely many hyperbolic manifolds with nonempty boundaries.
result Existence of incommensurable hyperbolic manifolds with a fixed perimeter-to-volume ratio.
Adapts RKHS methods to estimate density ratios with optimal error.
problem Estimating density ratios from limited data.
method Minimizes regularized Bregman divergence in RKHS, with Lepskii type parameter choice.
result Adaptive minimax optimal error rate for quadratic loss.
In this work, we propose new objective functions to train deep neural network based density ratio estimators and apply it to a change point detection problem. Existing methods use linear combinations of kernels to approximate the density ratio function by solving a convex constrained minimization problem. Approximating…
The Sharpe ratio is a way to compare the excess returns (over the risk free asset) of portfolios for each unit of volatility that is generated by a portfolio. In this paper we introduce a robust Sharpe ratio portfolio under the assumption that the risk free asset is unknown. We propose a robust portfolio that maximizes…