New compactification for character varieties with good topological properties.
problem Compactification of character varieties with good topological properties.
method Announced a new compactification with interpretations of ideal points.
result Relates to Weyl chamber length compactification and applies to maximal and Hitchin representations.
We investigate the structure of good deal bounds, which are subintervals of a no-arbitrage pricing bound, for financial market models with convex constraints as an extension of Arai and Fukasawa (2014). The upper and lower bounds of a good deal bound are naturally described by a convex risk measure. We call such a risk…
Linear groups without infinite order unipotents have good properties.
problem Properties of linear groups without unipotent elements of infinite order.
method Analyzing the structure and properties of linear groups without unipotent elements of infinite order.
result Linear groups without unipotent elements of infinite order have good properties, including centralisers virtually splitting and finitely generated abelian subgroups being undistorted.
The Ekeland variational principle implies what can be regarded as a strong version, in the C1 category, of the Yau minimum principle: under the appropriate hypotheses {\it every} minimizing sequence admits a {\it good shadow}, a second minimizing sequence that has good properties and is asymptotic to the original on…
We study convex risk measures describing the upper and lower bounds of a good deal bound, which is a subinterval of a no-arbitrage pricing bound. We call such a convex risk measure a good deal valuation and give a set of equivalent conditions for its existence in terms of market. A good deal valuation is characterized …
We analyze consistency of α-Rényi approximate posteriors for Bayesian models.
problem Consistency of variational Bayesian methods for intractable posteriors.
method We study α-Rényi approximate posteriors, focusing on α>1 and characterizing good sequences. result Sufficient conditions for consistency are identified, including the existence of a good sequence of distributions.
This study calculates the maximum error of a famous estimation method.
problem Estimating rare items not seen in a sample.
method Characterizes the maximal mean-squared error of the Good-Turing estimator.
result Characterizes the maximal mean-squared error of the Good-Turing estimator.
In this note we establish estimates for the harmonic map heat flow from S1 into a closed manifold, and use it to construct sweepouts with the following good property: each curve in the tightened sweepout, whose energy is close to the maximal energy of curves in the sweepout, is itself close to a closed geodesic.
Two models are identified for robust cross-impact analysis.
problem Developing and validating cross-impact models that fit data and are well-behaved.
method Classified cross-impact models according to desirable properties and evaluated them on three asset classes.
result Only one model satisfies all desirable properties and is suitable for applications.
AlphaGo Zero is explained as a GAN system with good convergence properties.
problem Explaining the success of AlphaGo Zero in a new light.
method Qualitative analysis of AlphaGo Zero as a GAN system.
result AlphaGo Zero's success may not indicate a new AI generation.
Study robust hedging and valuation under combined uncertainty about asset price drifts and volatilities.
problem Robust hedging and valuation under uncertainty about asset price drifts and volatilities.
method Non-dominated multiple priors approach to model uncertainty, worst-case good-deal bounds, coherent risk measures, second-order backward stochastic differential equations.
result Characterization of hedging strategies and good-deal bounds via solutions to backward stochastic differential equations.
The paper establishes conditions for optimal sampling configurations on complex manifolds.
problem Finding optimal sampling configurations on complex manifolds.
method Analyzes point configurations on compact complex manifolds using tensor powers of Hermitian ample line bundles.
result Necessary and sufficient conditions for the existence of asymptotically Fekete sequences.
New representation theory for closed geodesic subflows.
problem Classifying representations with good geometric properties.
method Restricting to invariant closed geodesic subflows.
result Equivalent characterizations and properties of new representations.
We consider the problem of classification using similarity/distance functions over data. Specifically, we propose a framework for defining the goodness of a (dis)similarity function with respect to a given learning task and propose algorithms that have guaranteed generalization properties when working with such good fu…
Framework for assessing fairness across similar predictive models.
problem Fairness in predictive models across different groups.
method Develops a framework for characterizing fairness over the set of good models under selective labels.
result Framework can replace or audit models for better fairness properties.
New concept of relatively dominated representations for higher-rank groups.
problem Understanding geometric finiteness in higher-rank Lie groups.
method Introducing and analyzing relatively dominated representations.
result Groups admitting relatively dominated representations are relatively hyperbolic.
Unified neural network model for astro-particle physics predictions with coverage, systematics, and goodness-of-fit.
problem Lack of statistical uncertainties, coverage, systematic uncertainties, and goodness-of-fit in neural network predictions.
method KL-divergence objective for joint distribution of data and labels, conditional normalizing flows, amortized with neural networks.
result Unified supervised learning and VAEs under stochastic variational inference for event property predictions.
This paper constructs an algebra on a 3-torus with specific properties for fluid dynamics.
problem Constructing an algebraic structure on a 3-torus with specific properties.
method Combining combinatorial graded intersection algebra with Sullivan's and Lawrence-Sullivan-Ranade's subcomplexes.
result The construction of an algebra with specific properties on the 3-torus.
The paper introduces pseudo-quotients for algebraic actions and applies them to character varieties.
problem Characterizing algebraic actions and their quotients.
method Introducing pseudo-quotients as a weak version of quotients for algebraic actions, focusing on purely topological properties.
result Pseudo-quotients are unique up to virtual class in characteristic zero and can be used to compute character varieties.
We derive a new discrepancy statistic for measuring differences between two probability distributions based on combining Stein's identity with the reproducing kernel Hilbert space theory. We apply our result to test how well a probabilistic model fits a set of observations, and derive a new class of powerful goodness-o…
Extends positive and almost positive links to successively almost positive ones.
problem Extending properties of positive and almost positive diagrams and links.
method Introducing successively almost positive diagrams and links, and analyzing their properties.
result Improves known results of positive and almost positive links.
In this paper we prove that RAAGs are distinguished from each other by their pro-p completions for any choice of prime p, and that RACGs are distinguished from each other by their pro-2 completions. We also give a new proof that hyperbolic virtually special groups are good in the sense of Serre. Furthermore we give…
Column normalization doesn't ensure good sparse recovery for random matrices.
problem Ensuring good sparse recovery properties for column-normalized random matrices.
method Constructing a random vector and showing that column normalization doesn't lead to desired recovery properties.
result Column-normalized random matrices do not satisfy exact reconstruction property with high probability.
The κ-generalised distribution fits daily stock returns well.
problem Stock returns are often heavy-tailed, not normally distributed.
method Used the κ-generalised distribution with a Monte-Carlo goodness of fit test. result The κ-generalised distribution fits historic daily stock returns well for a significant proportion of analyzed stocks. The abstract constructs a set of bad 3-orbifolds and shows how any bad 3-orbifold can be transformed into a good one.
problem Characterizing and transforming bad 3-orbifolds into good ones.
method Explicit construction of bad 3-orbifolds and a method of cutting-and-capping to transform them.
result Any bad 3-orbifold can be transformed into a good 3-orbifold through a finite number of operations.
A new test assesses how well observed networks fit a specified ERGM model.
problem Testing the goodness of fit for ERGMs with a single network observation.
method Kernel Stein discrepancy combined with a discrete Stein operator for ERGMs, Monte Carlo simulation.
result The test provides theoretical and practical support for assessing ERGM fit.
Optimal tests for goodness of fit and two-sample problems using MMD and KSD.
problem Asymptotically optimal tests for goodness of fit and two-sample problems.
method Maximum Mean Discrepancy (MMD) and Kernel Stein Discrepancy (KSD) based tests.
result Optimal tests achieve the maximum exponential decay rate under specific conditions.
The paper shows exchanging estimates over networks is effective for learning sparse signals.
problem Learning sparse signals over networks with limited communication.
method Iterative algorithm exchanging intermediate estimates over a network, with theoretical and simulation analysis.
result The iterative algorithm provides competitive performance in learning sparse signals.
Optimal persuasion involves projecting state vectors onto lower-dimensional 'optimal information manifolds'.
problem Optimal persuasion of another agent observing multi-dimensional data.
method Performing non-linear dimension reduction by projecting state vectors onto the 'optimal information manifold'.
result Optimal information design splits information into 'good' and 'bad' components, revealing only the direction of good information.
A new framework improves kernel Stein discrepancy tests for validating distributions.
problem Improving goodness-of-fit testing for non-normal distributions.
method Introducing Sf-KSD, a unifying framework for studying Stein operators in KSD-based tests.
result Sf-KSD guides the development of new tests and outperforms existing methods.
Kernel ridgeless regression with random features shows good generalization without explicit regularization.
problem Generalization of kernel ridgeless regression without explicit regularization.
method Investigation of ridgeless regression with random features and stochastic gradient descent, exploring the effect of random features error and spectral density optimization.
result Random features error exhibits the double-descent curve, leading to improved generalization.
New algorithm finds optimal sample complexity for pure exploration with multiple good answers.
problem Determining the optimal number of samples needed to explore multiple good answers in a bandit problem.
method Derive lower bound using game equilibrium, extend Track-and-Stop algorithm to multiple answers.
result New algorithm has asymptotic sample complexity matching the derived lower bound.
KSDAgg combines multiple KSD tests to improve goodness-of-fit testing without splitting data.
problem Improving goodness-of-fit testing without data splitting.
method KSDAgg aggregates multiple KSD tests with different kernels to maximize power.
result KSDAgg achieves the smallest uniform separation rate of the collection, up to a logarithmic term.
Regime-switching models, in particular Hidden Markov Models (HMMs) where the switching is driven by an unobservable Markov chain, are widely-used in financial applications, due to their tractability and good econometric properties. In this work we consider HMMs in continuous time with both constant and switching volati…
Two new tests assess how well conditional models fit data.
problem Assessing goodness of fit for conditional distributions.
method Nonparametric statistical tests using Stein operators.
result Tests are consistent and interpretable.
Lottery tickets find good initializations for IMP with sparse training.
problem Finding good initializations for iterative magnitude pruning (IMP) in sparse networks.
method Empirical study of IMP performance with varying pre-training data and iterations.
result Training on a small fraction of data suffices to obtain good initializations for IMP.
Unified approach amplifies data for distribution property estimation.
problem Estimating properties of discrete distributions efficiently.
method Unified, linear-time, competitive estimator using just 2n samples.
result Achieves performance of empirical estimator with n√log n samples using only 2n samples.
We study properties of irreducible and completely reducible representations of finitely generated groups Gamma into reductive algebraic groups G in in the context of the geometric invariant theory of the G-action on Hom(Gamma,G) by conjugation. In particular, we study properties of character varieties, X_G(Gamma)=Hom(G…
WeSpeR speeds up non-linear shrinkage for high-dimensional weighted covariance.
problem Computing non-linear shrinkage formulas for high-dimensional weighted sample covariance.
method Derive extit{WeSpeR} algorithm using asymptotic sample spectrum properties.
result Significantly speeds up non-linear shrinkage in dimensions higher than 1000.
New test assesses probabilistic model calibration without expensive approximations.
problem Assessing calibration of probabilistic models with scores.
method Kernel Calibration Conditional Stein Discrepancy (KCCSD) test using new score-based kernels.
result Control over type-I error with improved scalability and efficiency.
Gaussian kernel tests are optimal against smooth alternatives.
problem Understanding the statistical properties of nonparametric tests using Gaussian kernels.
method Analysis of Gaussian kernel-based goodness-of-fit, homogeneity, and independence tests.
result Gaussian kernel tests are minimax optimal against smooth alternatives in all three settings.
Develops a universal test for assessing dynamic network models.
problem Determine if observed networks match a candidate dynamic random graph model.
method Formulates and analyzes a universal test for graph-valued, infinite-state Markov processes.
result Exhibits and analyzes a universal test for a natural class of models.
The aim of this paper is two-fold: first, we look at the fractional Laplacian and the conformal fractional Laplacian from the general framework of representation theory on symmetric spaces and, second, we construct new boundary operators with good conformal properties that generalize the fractional Laplacian using an e…
Paper introduces a method to explain deep learning models and identify good generalization.
problem Limited interpretability of neural networks hinders progress and real-world applications.
method Polytope interpolation method for local explainability and generalization assessment.
result Developed a method to identify deep learning models with good generalization properties.
This paper reviews some of the phenomenological models which have been introduced to incorporate the scaling properties of financial data. It also illustrates a microscopic model, based on heterogeneous interacting agents, which provides a possible explanation for the complex dynamics of markets' returns. Scaling and m…
Any closed, oriented, hyperbolic three-manifold with nontrivial second homology has many quasigeodesic flows, where quasigeodesic means that flow lines are uniformly efficient in measuring distance in relative homotopy classes. The flows are pseudo-Anosov flows which are almost transverse to finite depth foliations in …
Improved molecular property prediction using WL embedding in GNNs.
problem Limited performance of GNNs in predicting molecular properties.
method Explored Weisfeiler-Lehman (WL) embedding to replace GNN layers, enhancing representability and performance.
result WL embedding consistently improves GNN performance across multiple datasets.
Random deep neural networks favor simple functions.
problem Understanding the generalization properties of deep learning.
method Analyzing binary classifiers of random wide deep neural networks with ReLU activation.
result Random deep neural networks are biased towards simple functions.