New DKPP family controls positive and negative dependence in random subsets.
problem Challenges in seamlessly bridging probabilistic models for positive and negative dependence.
method Introduced DKPP family and developed computational methods for probabilistic operations and inference.
result Controllability of positive and negative dependence demonstrated through numerical experiments.
Study ranking in generalized linear bandits with position and item dependencies.
problem Complex reward function due to position and item dependencies in recommendation systems.
method Model position and item dependencies, design UCB and Thompson Sampling algorithms.
result Generalizes existing studies in position dependencies and graph theory.
In this paper, we prove a differential Harnack inequality for positive solutions of time-dependent heat equations with potentials. We also prove a gradient estimate for the positive solution of the time-dependent heat equation.
We develop Square Root Graphical Models (SQR), a novel class of parametric graphical models that provides multivariate generalizations of univariate exponential family distributions. Previous multivariate graphical models [Yang et al. 2015] did not allow positive dependencies for the exponential and Poisson generalizat…
We introduce two types of ordinal pattern dependence between time series. Positive (resp. negative) ordinal pattern dependence can be seen as a non-paramatric and in particular non-linear counterpart to positive (resp. negative) correlation. We show in an explorative study that both types of this dependence show up in …
New method for PU learning with instance-dependent propensity scores.
problem Learning from positive and unlabeled data with instance-dependent labeling.
method Empirical risk minimization of joint risk function, alternating optimization of posterior probability and propensity score.
result The method achieves comparable or better performance than state-of-the-art methods.
The paper proves finite Urysohn 1-width for 4 and 5 manifolds with positive biRicci curvature.
problem Proving finite Urysohn 1-width for 4 and 5 manifolds with positive biRicci curvature.
method Using positive biRicci curvature and uniform scalar curvature bounds, the paper shows that the Urysohn 1-width is finite and depends only on the curvature bounds.
result Closed 4 and 5 manifolds with positive biRicci curvature have finite Urysohn 1-width, which depends only on the curvature bounds.
The paper examines how small positive dependence can lead to correlated tail risks.
problem Understanding the impact of dependence uncertainty on tail risk measures.
method Introducing a regular dependence measure and analyzing the aggregation of risks.
result Small positive dependence can result in perfectly correlated tail risks.
We investigate how the local fluctuations of the signed traded volumes affect the dependence of demands between stocks. We analyze the empirical dependence of demands using copulas and show that they are well described by a bivariate K copula density function. We find that large local fluctuations strongly …
We show that a wide range of overdetermined boundary problems for semilinear equations with position-dependent nonlinearities admits nontrivial solutions. The result holds true both on the Euclidean space and on compact Riemannian manifolds. As a byproduct of the proofs we also obtain some rigidity, or partial symmetry…
The paper tests if optimal hedge ratios for Bitcoin are position-dependent.
problem Testing if optimal hedge ratios for Bitcoin are position-dependent.
method Explicit and efficient method for testing symmetric vs. asymmetric optimal hedge ratios in a multivariate setting.
result The optimal hedge ratio for Bitcoin is position-dependent, with long positions having a higher ratio than short positions.
New method models stopping times that can be equal with non-zero probability.
problem Standard stopping time models assume conditional independence, limiting flexibility.
method Modified Cox construction with bivariate exponential distribution.
result Created a family of stopping times that can be equal with positive probability.
Develops a new model for measuring extremal dependence in financial markets.
problem Lack of suitable models for studying extremal dependence in financial markets.
method Constructs regular variation models on Rd and develops a bivariate measure for asymmetry in extremal dependence. result Rejects the Efficient Tail Hypothesis for China's futures market and identifies profitable investment opportunities.
We propose an iterative scheme for feature-based positioning using a new weighted dissimilarity measure with the goal of reducing the impact of large errors among the measured or modeled features. The weights are computed from the location-dependent standard deviations of the features and stored as part of the referenc…
Satellite links of fully positive braids are characterized.
problem Characterizing satellite links of fully positive braids.
method Analyzing fully positive braids and their satellites.
result Satellite links of fully positive braids are characterized by specific conditions.
Max-rank improves multiple testing in conformal prediction.
problem Simultaneous testing of multiple hypotheses in scientific inquiries.
method Introduces max-rank, a novel correction for positive dependencies in simultaneous testing.
result Max-rank efficiently controls family-wise error rate and improves predictive uncertainty estimates.
New findings control FDR for online testing methods under positive dependence.
problem Maintaining FDR control for online testing methods under positive dependence.
method Developed new methods to control FDR for online testing procedures under positive dependence.
result SAFFRON and LORD control FDR under positive dependence, not just conditional superuniformity.
In this paper, we mainly study the mean curvature flow in Kähler surfaces with positive holomorphic sectional curvatures. We prove that if the ratio of the maximum and the minimum of the holomorphic sectional curvatures is less than 2, then there exists a positive constant δ depending on the ratio such that $\cosα\ge…
Study replicates reference-dependent preferences impact on risk-return trade-off in Chinese stock market.
problem Impact of reference-dependent preferences on risk-return trade-off in Chinese stock market.
method Utilized CGO proxy, econometric techniques (Dependent Double Sorting, Fama-MacBeth regressions), and data from 1995-2024.
result Reference-dependent preferences have a weaker or absent positive risk-return relationship in the Chinese market.
In this paper, we give a new generalization of positive sectional curvature called positive weighted sectional curvature. It depends on a choice of Riemannian metric and a smooth vector field. We give several simple examples of Riemannian metrics which do not have positive sectional curvature but support a vector field…
The paper studies the number of normals to ellipsoids and their intersections with caustics.
problem The number of normals to an ellipsoid passing through a given point.
method Intersection points of the ellipsoid and its caustics are used to study the problem in 3D space.
result The number of normals is dependent on the position of the given point with respect to the caustics of the ellipsoid.
When learning from positive and unlabelled data, it is a strong assumption that the positive observations are randomly sampled from the distribution of X conditional on Y=1, where X stands for the feature and Y the label. Most existing algorithms are optimally designed under the assumption. However, for many real…
New method for robust financial portfolio analysis.
problem Challenges in modeling financial portfolio dependence structure.
method Nonparametric Angles-based Correlation (NAbC) method.
result Valid inferences and flexible scenarios for portfolio analysis.
Bitcoin reacts positively to USDT minting but not burning, showing state-dependence.
problem Understanding Bitcoin's response to Tether's supply changes.
method Analyzing Bitcoin's intraday price movements in response to USDT minting and burning events.
result Bitcoin's response to USDT minting events declines after 60 minutes and is influenced by investor sentiment and public announcements.
Upper diameter bound for manifolds with positive scalar curvature.
problem Estimating the maximum size of manifolds with positive scalar curvature.
method Proving an upper diameter bound using scalar curvature integral, Yamabe constant, and manifold dimension.
result The power of scalar curvature integral in diameter estimates is sharp and occurs at round spheres with canonical metric.
Study proves existence, uniqueness, and positivity of solutions to a complex volatility model.
problem Modeling equity index and spot volatility with path-dependent features and general kernels.
method Proved existence and uniqueness of a continuous solution to a Stochastic Volterra Equation (SVE) with non-convolutional, non-bounded kernels and non-Lipschitz coefficients.
result Positivity of the volatility process under certain conditions on the kernels.
New inequalities for matrix supermartingales converge under various conditions.
problem Convergence and maximal inequalities of supermartingales in positive semidefinite matrices.
method Developed new concentration inequalities for matrix supermartingales.
result New inequalities for matrix supermartingales under different tail conditions.
Proposes a new VIX futures trading strategy based on term structure modeling.
problem Optimizing VIX futures trading based on term structure.
method Assumes VIX futures term structure follows a Markov model. Uses a deep neural network to model the functional dependence between VIX futures curve, positions, and expected utility.
result Backtests show reasonable portfolio performance and optimal long/short positions.
We discuss a simple extension of the Ho and Lee model with generic time-dependent drift in which: 1) we compute bond prices analytically; 2) the yield curve is sensible and the asymptotic yield is positive; and 3) our analytical solution provides a clean and simple way of separating volatility from the drift in the sho…
We show the existence of uniformly bounded sequences of increasing numbers of orthonormal sections of powers Lk of a positive holomorphic line bundle L on a compact Kähler manifold M. In particular, we construct for each positive integer k, orthonormal sections s1k,…,snkk in H0(M,Lk), $n_k\geβ…
Investigates portfolio selection for rank-dependent utilities in incomplete markets.
problem Portfolio selection for agents with rank-dependent utility in incomplete financial markets.
method Characterizes deterministic strict equilibrium strategies for constant-coefficient and time-invariant probability weighting functions. Addresses the issue of selecting an optimal strategy from multiple equilibrium strategies for time-variant probability weighting functions.
result Characterizes deterministic strict equilibrium strategies and identifies optimal strategies from multiple equilibrium strategies.
Let [γ] be the conformal boundary of a warped product C3,α AHE metric g=gM+u2h on N=M×F, where (F,h) is compact with unit volume and nonpositive curvature. We show that if [γ] has positive Yamabe constant, then u has a positive lower bound that depends only on [γ].
Spectral sparsification improves Gaussian graphical models under MTP2 constraints.
problem Learning accurate, sparse graphs from data under MTP2 constraints.
method Spectral graph sparsification applied to Gaussian graphical models.
result Spectral-MTP2 preserves MTP2 and approximates the original model well.
We show how to associate with each graph with a certain property (positivity) a family of simply connected solvable Lie groups endowed with left-invariant Riemannian metrics that are Ricci solitons (called solsolitons). We classify them up to isometry, obtaining families depending on many parameters of explicit example…
Introduces a new Hawkes model with CARMA(p,q) intensity to better model dependence structures.
problem Modeling dependence structures in time series data with realistic autocorrelation functions.
method Develops a Hawkes process with CARMA(p,q) intensity to capture more complex dependencies.
result The CARMA(p,q)-Hawkes model can reproduce more realistic dependence structures and is stationary and positive.
Minimal splitting factors help study scalar curvature constraints.
problem Scalar curvature constraints in geometry.
method Introducing minimal splitting factors with positive scalar curvature.
result Minimal splitting factors have properties similar to area minimizing hypersurfaces.
Adaptive source selection for positive transfer in linear models improves target dataset performance.
problem Limited task-specific labeled data in business settings.
method Greedily decides from which sources and how many samples to incorporate into the target dataset using an accept/reject rule based on a data-dependent estimate of the transfer gain.
result Consistent gains over classical and recent strong baselines while avoiding negative transfer.
Learning a classifier with control on the false-positive rate plays a critical role in many machine learning applications. Existing approaches either introduce prior knowledge dependent label cost or tune parameters based on traditional classifiers, which lack consistency in methodology because they do not strictly adh…
Study on predicting graph labels at nodes using local averaging and distance estimation.
problem Predicting graph labels at nodes given observations at other nodes.
method Local averaging and distance estimation methods for graph regression.
result Alternative methods can achieve standard nonparametric rates even when graph neighborhoods are too large or small.
A new method predicts true classes from positive and unlabeled data with additional labeled observations.
problem Predicting true classes from positive and unlabeled data with selection bias.
method Introduces augmented PU prediction, allowing feature-dependent labeling, and compares various empirical Bayes rules.
result The variational autoencoder-based method performs similarly or better than other methods and improves accuracy for unlabeled samples.
New concept of partial comonotonicity connects riskmetrics and dependence.
problem Understanding and quantifying risk metrics under partial comonotonicity.
method Developed a new notion of partial comonotonicity and established its connection to distortion riskmetrics.
result Partial comonotonicity uniquely characterizes a class of distortion riskmetrics through additivity.
We show that the notion of 3-hyperconvexity on oriented flag manifolds defines a partial cyclic order. Using the notion of interval given by this partial cyclic order, we construct Schottky groups and show that they correspond to images of positive representations in the sense of Fock and Goncharov. We construct poly…
The regulator is interested in proposing a capital adequacy test by specifying an acceptance set for firms' capital positions at the end of a given period. This set needs to be surplus-invariant, i.e., not to depend on the surplus of firms' shareholders, because the test means to protect firms' liability holders. We pr…
We demonstrate both analytically and numerically that the existing methods for measuring tail dependence in copulas may sometimes underestimate the extent of extreme co-movements of dependent risks and, therefore, may not always comply with the new paradigm of prudent risk management. This phenomenon holds in the conte…
The paper provides gradient estimates for a specific equation on Riemannian manifolds.
problem Gradient estimates for positive solutions to a specific equation on Riemannian manifolds.
method Obtained gradient bounds for positive solutions without depending on the solution's bounds or the Laplacian of the distance function.
result Gradient bound of a positive solution does not depend on the solution's bounds or the Laplacian of the distance function.
Optimizes leveraged staking strategies in decentralized finance.
problem Maximizing returns on staked assets in decentralized lending platforms.
method Developed a mathematical framework to optimize leveraged staking strategies, reducing the multi-market problem to convex allocation over market exposures.
result Rebalanced leveraged positions can achieve up to 6.2% APY, significantly higher than unleveraged staking.
Proves positive mass theorem for spin initial data sets with arbitrary ends and dominant energy shields.
problem Proving the positive mass theorem for spin initial data sets with various ends and energy shields.
method Modification of Witten's approach involving an additional independent timelike direction in the spinor bundle.
result Positive mass theorem for spin initial data sets with arbitrary ends and dominant energy shields.
This paper examines quantile dependence between international stock markets and evaluates its use for improving volatility forecasting. First, we analyze quantile dependence and directional predictability between the US stock market and stock markets in the UK, Germany, France and Japan. We use the cross-quantilogram, …