Study on discrete Okounkov bodies and their applications.
problem Understanding stability and thresholds in higher dimensions.
method Analysis of discrete Okounkov bodies and gap phenomena.
result Asymptotic analysis of stability and thresholds.
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A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,051 papers · 148 categories
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48 results for “discretization thresholds”
A new algorithm infers causal networks from data using topological thresholds.
problem Inferring causal networks from data.
method Two methods for determining topological thresholds: one to leave no disconnected nodes, the other to find a causal large connected component.
result The novel algorithm is faster and more accurate than the PC algorithm.
Discrete time hedging in a complete diffusion market is considered. The hedge portfolio is rebalanced when the absolute difference between delta of the hedge portfolio and the derivative contract reaches a threshold level. The rate of convergence of the expected squared hedging error as the threshold level approaches z…
The health state assessment and remaining useful life (RUL) estimation play very important roles in prognostics and health management (PHM), owing to their abilities to reduce the maintenance and improve the safety of machines or equipment. However, they generally suffer from this problem of lacking prior knowledge to …
Neural regression trees convert regression to classification more effectively.
problem Suboptimal approaches for regression via classification.
method Joint optimization framework for learning optimal discretization thresholds and feature selection in a neural regression tree.
result Empirically validated as state-of-the-art on challenging regression tasks.
We relax demographic parity in regression by enforcing parity at quantile levels and score thresholds.
problem Enforcing full distributional fairness in regression can lead to substantial accuracy loss.
method Introduce (, Z)-fair predictor, derive closed-form solutions, and develop post-processing algorithm.
result The risk gap to the continuous optimum vanishes as the grid is refined, and we enable targeted fairness corrections.
We study the motion of discrete interfaces driven by ferromagnetic interactions in a two-dimensional periodic environment by coupling the minimizing movements approach by Almgren, Taylor and Wang and a discrete-to-continuous analysis. The case of a homogeneous environment has been recently treated by Braides, Gelli and…
New theorem on graph curvature thresholds and uniqueness.
problem Determining the minimum number of edges for graphs to have positive curvature.
method Analyzing graphs with specific edge counts and curvature properties.
result Optimal threshold for positive curvature and uniqueness of extremal graphs.
FILTER model uses fusion penalized logistic threshold regression for high-dimensional data with unknown cut points.
problem Modeling high-dimensional data with unknown cut points and binary responses.
method Fusion penalized logistic threshold regression (FILTER) model with fused lasso penalty for variable selection.
result Established non-asymptotic error bounds for coefficient estimation and model selection consistency.
We consider a univariate semimartingale model for (the logarithm of) an asset price, containing jumps having possibly infinite activity (IA). The nonparametric threshold estimator of the integrated variance IV proposed in Mancini 2009 is constructed using observations on a discrete time grid, and precisely it sums up t…
Strong convergence of the thresholding scheme for the mean curvature flow of mean convex setsmath.AP
Study shows thresholding scheme converges for mean curvature flow of convex sets.
problem Analyzing convergence of thresholding scheme for mean curvature flow.
method Time discretization using Merriman, Bence and Osher's scheme, focusing on two-phase mean convex settings.
result Time-integrated energy of approximation converges to limit's energy in minimizing movements interpretation.
Variable selection in linear models plays a pivotal role in modern statistics. Hard-thresholding methods such as regularization are theoretically ideal but computationally infeasible. In this paper, we propose a new approach, called the LAGS, short for "least absulute gradient selector", to this challenging yet i…
We investigate how and when to diversify capital over assets, i.e., the portfolio selection problem, from a signal processing perspective. To this end, we first construct portfolios that achieve the optimal expected growth in i.i.d. discrete-time two-asset markets under proportional transaction costs. We then extend ou…
We consider the problem of the optimal trading strategy in the presence of linear costs, and with a strict cap on the allowed position in the market. Using Bellman's backward recursion method, we show that the optimal strategy is to switch between the maximum allowed long position and the maximum allowed short position…
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.
To date, attribute discretization is typically performed by replacing the original set of continuous features with a transposed set of discrete ones. This paper provides support for a new idea that discretized features should often be used in addition to existing features and as such, datasets should be extended, and n…
Identifying the covariation between the diffusion parts and the co-jumps given discrete observationsmath.PR
In this paper we consider two semimartingales driven by diffusions and jumps. We allow both for finite activity and for infinite activity jump components. Given discrete observations we disentangle the {\it integrated covariation} (the covariation between the two diffusion parts, indicated by IC) from the co-jumps. Thi…
New method converts conventional ANNs to SNNs with minimal loss and efficiency.
problem Difficulty in training SNNs directly from conventional ANNs due to discreteness.
method Proposes a novel pipeline combining threshold balance and soft-reset mechanisms for efficient conversion.
result Achieves almost no accuracy loss with only 1/10 of typical SNN simulation time.
We study the motion of discrete interfaces driven by ferromagnetic interactions in a two-dimensional low-contrast periodic environment, by coupling the minimizing movements approach by Almgren, Taylor and Wang and a discrete-to-continuum analysis. As in a recent paper by Braides and Scilla dealing with high-contrast pe…
We study optimal investment in a financial market having a finite number of assets from a signal processing perspective. We investigate how an investor should distribute capital over these assets and when he should reallocate the distribution of the funds over these assets to maximize the cumulative wealth over any inv…
We apply a utility-based method to obtain the value of a finite-time investment opportunity when the underlying real asset is not perfectly correlated to a traded financial asset. Using a discrete-time algorithm to calculate the indifference price for this type of real option, we present numerical examples for the corr…
DRCD identifies causal direction between continuous and discrete variables using density ratio monotonicity.
problem Inferring causal direction between continuous and discrete variables from observational data.
method Density Ratio-based Causal Discovery (DRCD) method.
result DRCD identifies causal direction between continuous and discrete variables using density ratio monotonicity.
A natural approach to analyze interaction data of form "what-connects-to-what-when" is to create a time-series (or rather a sequence) of graphs through temporal discretization (bandwidth selection) and spatial discretization (vertex contraction). Such discretization together with non-negative factorization techniques c…
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.
As datasets grow richer, an important challenge is to leverage the full features in the data to maximize the number of useful discoveries while controlling for false positives. We address this problem in the context of multiple hypotheses testing, where for each hypothesis, we observe a p-value along with a set of feat…
New test SCI for conditional independence on discrete data improves accuracy in causal discovery.
problem Testing conditional independence on discrete data often fails in practice.
method Proposes a new test based on stochastic complexity for discrete data.
result SCI is an asymptotically unbiased and L2 consistent estimator for conditional mutual information (CMI).
New study shows diversification can increase risk for heavy-tailed losses.
problem Diversification can increase tail risk for heavy-tailed losses.
method Comparison of diversified portfolio to a 'one-basket' benchmark.
result Diversified portfolio has larger tail probabilities than a 'one-basket' benchmark for all thresholds.
A new method uses Coordinate Descent to optimize ResNet networks for private inference.
problem Reducing ReLU count in ResNet networks for private inference.
method Directly optimizing in the discrete domain using Coordinate Descent.
result Our method yields a sparse solution and is state-of-the-art.
Limit Order Book Dynamics in Matching Markets: Microstructure, Spread, and Execution Slippageq-fin.TR
The paper models market dynamics using a limit order book system to explain slippage and inefficiency.
problem Inefficiency in matching markets due to structural liquidity constraints and slippage.
method Introduces a market microstructure framework with a latent preference state matrix and a dynamic discrete choice execution model.
result Persistent slippage and regional invariance of preference orderings are explained by liquidity thresholds.
Technology Adoption and Network Externalities in Financial Systems: A Spatial-Network Approachecon.EM
Paper analyzes tech adoption in financial networks, finding key leadership and diffusion dynamics.
problem Understanding technology adoption and network effects in financial systems.
method Developed a spatial-network framework with a master equation and Feynman-Kac representation.
result Found strong support for two-regime adoption dynamics and significant leadership in network central banks.
We extend to the multi-asset case the framework of a discrete time model of a single asset financial market developed in Ghoulmie et al (2005). In particular, we focus on adaptive agents with threshold behavior allocating their resources among two assets. We explore numerically the effect of this diversification as an …
The trade-off between the cost of acquiring and processing data, and uncertainty due to a lack of data is fundamental in machine learning. A basic instance of this trade-off is the problem of deciding when to make noisy and costly observations of a discrete-time Gaussian random walk, so as to minimise the posterior var…
Study optimal policies under budget and coverage constraints.
problem Optimal policy learning with budget and coverage constraints.
method Combination of knapsack structure, affine threshold rule, linear programming relaxation, Greedy-Lagrangian (GLC), and rank-and-cut (RC) algorithms.
result GLC closely approximates the optimal solution and achieves near-optimal performance in finite samples; RC is approximately optimal under certain conditions.
We study the problem of learning influence functions under incomplete observations of node activations. Incomplete observations are a major concern as most (online and real-world) social networks are not fully observable. We establish both proper and improper PAC learnability of influence functions under randomly missi…
Extends probabilistic approach for Kahler-Einstein metrics on Fano manifolds.
problem Constructing Kahler-Einstein metrics on log Fano manifolds with non-discrete automorphism groups.
method Introduces Gibbs polystability and uses moment map constraint to break symmetry.
result Gibbs polystability conjectured to be equivalent to existence of Kahler-Einstein metric.
Iterative thresholding algorithms seek to optimize a differentiable objective function over a sparsity or rank constraint by alternating between gradient steps that reduce the objective, and thresholding steps that enforce the constraint. This work examines the choice of the thresholding operator, and asks whether it i…
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.
Paper proposes an efficient AL-GP method for CDF/CCDF estimation in UQ.
problem Estimating full probability distribution in forward UQ analysis.
method Active learning-based Gaussian process (AL-GP) metamodelling method.
result Efficient estimation of CDF/CCDF without explicit discretization.
Rates of Estimation of Optimal Transport Maps using Plug-in Estimators via Barycentric Projectionsmath.ST
The paper analyzes rates of convergence for optimal transport map estimators using barycentric projections.
problem Estimating optimal transport maps from data sampled according to two distributions.
method Comprehensive analysis of rates of convergence for plug-in estimators defined via barycentric projections.
result New stability estimate for barycentric projections under minimal smoothness assumptions.
This paper introduces the factorial marked temporal point process model and presents efficient learning methods. In conventional (multi-dimensional) marked temporal point process models, event is often encoded by a single discrete variable i.e. a marker. In this paper, we describe the factorial marked point processes w…
Estimates natural parameters of p-tensor Ising models efficiently.
problem Estimating natural parameters of p-tensor Ising models from a single sample.
method Maximum pseudo-likelihood (MPL) method.
result MPL estimate is sqrt(N)-consistent under various conditions.
Study on reinsurance decisions using mean-variance criterion with irreversible contracts.
problem Optimizing reinsurance premiums and contracts in a Stackelberg game with irreversible contracts.
method Unified singular control framework applied to both discrete and continuous time reinsurance contracts.
result A single once-for-all reinsurance contract is preferred over multiple contracts, and the signing time is crucial.
Reflected Diffusion Modelsstat.ML
Reflected Diffusion Models improve on score-based models by incorporating data constraints.
problem Numerical error in score-based models leads to unnatural samples.
method Reverses a reflected stochastic differential equation on data support, learning perturbed score function through generalized score matching loss.
result Improves sample quality and fidelity without architectural modifications.
New algorithm for reinforcement learning in uncertain environments with unknown thresholds.
problem Safety in reinforcement learning in unknown and uncertain environments.
method Growing-Window estimator sampling and Stochastic Pessimistic-Optimistic Thresholding (SPOT) algorithm.
result Achieves sublinear regret and constraint violation of .
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.
Optimal Bubble Riding with Price-dependent Entry: a Mean Field Game of Controls with Common Noiseq-fin.MF
Study on optimal bubble riding with price-dependent entry times in a mean field game model.
problem Optimal bubble riding with price-dependent entry times.
method Mean field game of controls with common noise and random entry time, existence result obtained through discretization and limit analysis.
result Existence of equilibrium in the mean field game model.
Study stability thresholds of big line bundles, proving bounds and generalizing results.
problem Stability thresholds of big line bundles and their asymptotic behavior.
method Explicit bounds on error terms, using quasi-monomial valuations to compute stability thresholds.
result Proves Jin--Rubinstein--Tian's questions affirmatively.
Adaptive algorithm for outlier detection by balancing arm exploration and threshold estimation.
problem Identifying outliers in a set of rewards where the threshold is a function of all rewards.
method Adaptively updated confidence interval for the threshold based on previous rounds' estimates, balancing exploration of individual arms and the outlier threshold.
result Efficient algorithm with reduced sample complexity for outlier detection.