New definition of MCVaR for discrete probability spaces.
problem Existing definitions of MCVaR not suitable for discrete random variables.
method Proposes vector-valued MCVaR (VMCVaR) for discrete probability spaces.
result VMCVaR provides advantages over existing definitions for discrete cases.
Study shows financial value of weak information converges in discrete vs continuous markets.
problem Analyzing financial value of weak information in discrete vs continuous markets.
method Defined minimal probability measure and financial value of weak information, then showed convergence.
result Financial value of weak information converges in discrete vs continuous markets.
A new discrete calculus for bundle-valued forms is proposed and validated.
problem Discretization of exterior calculus for bundle-valued forms.
method Discretization of Cartan's exterior calculus for differential forms with values in vector bundles.
result The proposed discrete operator mimics the continuous exterior covariant derivative and ensures numerical convergence.
Paper proves a discrete Schwarz-Pick lemma for generalized circle packings.
problem Comparing geometric quantities of circle packings with different boundary values.
method Combinatorial Calabi flows and maximum principle.
result Discrete Schwarz-Pick lemma proven for generalized circle packings.
Study on 2-valued dynamics on complex plane, showing some dynamics can't be group actions.
problem Whether 2-valued dynamics can be defined by the action of a 2-valued group.
method Construction of examples of dynamics that are or are not group actions.
result Some 2-valued dynamics on complex plane cannot be defined by the action of a 2-valued group.
New RL algorithm tackles complex discrete action spaces.
problem Challenges in applying on-policy RL in high-dimensional discrete action spaces.
method Action-value critic, correlated actions, gradient sparsification.
result Empirically outperforms related on-policy algorithms.
Develops combinatorial theory of vector bundles on simplicial complexes.
problem Creating a discrete theory for vector bundles and connections on simplicial complexes.
method Introduces discrete exterior covariant derivative and applies it to various geometric objects.
result Flat discrete connections yield a cochain complex computing twisted de Rham cohomology.
New model clusters discrete time series data.
problem Handling discreteness and time series properties in data.
method Finite mixture model with INAR type models.
result Demonstrated clustering on real data.
Researchers found a formula for the value of knowing stock price distributions in discrete models.
problem Determining the financial value of stock price information in discrete market models.
method Derived an explicit formula for weak information value in a discrete time model with complete markets.
result Explicit calculations for binomial and trinomial models show the formula's applicability.
Combines linear acyclic model with logistic regression for causal structure estimation from mixed data.
problem Estimating causal structure from mixed continuous and discrete data.
method Defines a hybrid causal model combining linear acyclic model for continuous variables and logistic regression for discrete variables. Derives BIC scoring function for model selection. Employs a new discovery algorithm to learn causal structures without discretization.
result Empirically demonstrates the power of the method through simulations.
This paper morphs images on manifold-valued spaces using discrete geodesics.
problem Morphing manifold-valued images with discrete geodesics.
method Time discrete geodesic paths model, numerical minimization alternating between deformations and images.
result Existence of minimizing sequences for morphing manifold-valued images.
Discrete Lagrange problems solved with Lie group constraints.
problem Solving discrete Lagrange problems with Lie group constraints.
method Proving critical sections are solutions of unconstrained variational problems, applying Noether theory and multisymplectic forms.
result Critical sections of discrete Lagrange problems are solutions of unconstrained variational problems.
We present an explicit formula for the discrete power function introduced by Bobenko, which is expressed in terms of the hypergeometric τfunctions for the sixth Painlevé equation. The original definition of the discrete power function imposes strict conditions on the domain and the value of the exponent. However, we sh…
New finite element method for complex forms in any dimension.
problem Discretization of complex forms in arbitrary dimensions.
method Finite element discretization of ℓ-form-valued k-forms on triangulations. result Generalizes existing finite element methods for various tensor fields.
In the context of a Black-Scholes economy and with a no-arbitrage argument, we derive arbitrarily accurate lower and upper bounds for the value of European options on a stock paying a discrete dividend. Setting the option price error below the smallest monetary unity, both bounds coincide, and we obtain the exact value…
This work develops discrete Gaussian models for vector-valued data on triangular meshes.
problem Discrete representation of continuous vector-valued environmental data.
method Develops discrete intrinsic Gaussian processes for vector-valued data on triangular meshes using discrete differential operators.
result Models can capture harmonic flows, incorporate boundary conditions, and model non-stationary data.
Discretizing input space improves DLN robustness against adversarial attacks.
problem Improving machine learning models' resistance to adversarial attacks.
method Input discretization and Binary Neural Networks (BNNs).
result 2-bit input discretization significantly enhances adversarial robustness with minimal accuracy loss.
This work extends set-valued risk measures to discrete time, using difference inclusions and equations.
problem Defining set-valued dynamic risk measures in discrete time.
method Investigates discrete time setting with difference inclusions and difference equations.
result Provides insights for continuous time representations of set-valued dynamic risk measures.
Paper analyzes stability of discrete-time hypercomplex-valued Hopfield neural networks.
problem Stability of discrete-time hypercomplex-valued Hopfield neural networks.
method Introduces real-part associative hypercomplex number systems and B-projection functions to ensure stability. result Stability analysis of several discrete-time hypercomplex-valued Hopfield-type neural networks confirmed.
Constructs unique bases for CY varieties over valued fields.
problem Finding unique bases for CY varieties over valued fields.
method Uses techniques from higher rank degenerations in K-stability.
result Induces canonical functions on skeletons and agrees with tropicalizations of theta functions.
New algorithm adds discretized features to improve predictive models.
problem Improving predictive models using continuous features.
method D-MIAT algorithm for supervised discretization and feature extension.
result Combination of original data and D-MIAT-generated features yields best predictive performance.
Our aim in this paper is to provide a theory of discrete Riemann surfaces based on quadrilateral cellular decompositions of Riemann surfaces together with their complex structure encoded by complex weights. Previous work, in particular of Mercat, mainly focused on real weights corresponding to quadrilateral cells havin…
Defines market-consistent value of insurance liabilities under capital requirements.
problem Value of insurance liabilities subject to repeated capital requirements.
method Optimal stopping problems and backward recursion to compute value.
result Defines the value of insurance liabilities as no-arbitrage price optimally stopped.
We address the problem of classifying discrete differential-geometric Poisson brackets (dDGPBs) of any fixed order on target space of dimension 1. It is proved that these Poisson brackets (PBs) are in one-to-one correspondence with the intersection points of certain projective hypersurfaces. In addition, they can be re…
The paper proposes a variational autoencoder for discrete data analysis.
problem Sparse, high-dimensional, and overdispersed discrete data analysis.
method Variational autoencoder based on negative-binomial distribution.
result The proposed models achieve significantly better performance on text analysis, collaborative filtering, and multi-label learning compared to state-of-the-art baselines.
Adaptive discretization improves model-based RL in large spaces.
problem Efficient model-based reinforcement learning in large state-action spaces.
method Optimistic one-step value iteration with adaptive discretization.
result Adaptive discretization leads to better performance and lower memory usage.
The paper improves privacy accounting for discrete-valued mechanisms and the subsampled Gaussian mechanism.
problem Improving the accuracy and efficiency of differential privacy accounting for discrete outputs.
method Uses fast Fourier transform (FFT) for rigorous error analysis and accounting of privacy loss.
result Provides strict lower and upper bounds for (ε,δ)-values, demonstrating up to 75% reduction in noise variance. This paper derives a diffusion approximation for a sequence of discrete-time one-sided limit order book models with non-linear state dependent order arrival and cancellation dynamics. The discrete time sequences are specified in terms of an R+-valued best bid price process and an Lloc2-valued volume process. …
We study an optimal execution problem with uncertain market impact to derive a more realistic market model. We construct a discrete-time model as a value function for optimal execution. Market impact is formulated as the product of a deterministic part increasing with execution volume and a positive stochastic noise pa…
A new method for efficiently estimating Shapley values in dataset valuation.
problem Quantifying the incremental gain of individual datasets in machine learning tasks.
method Discrete uniform Shapley value approximation.
result Proposes a more efficient method for Shapley value estimation.
Defines discrete symmetry of manifolds and proves bounds on its value.
problem Understanding the symmetry of manifolds and proving bounds on their discrete symmetry.
method Defining discrete degree of symmetry and proving bounds using effective actions of groups.
result Proves disc−sym(X)≤3n/2 for connected manifolds and provides evidence for disc−sym(X)≤n. In this paper we present a nonparametric method for extending functional regression methodology to the situation where more than one functional covariate is used to predict a functional response. Borrowing the idea from Kadri et al. (2010a), the method, which support mixed discrete and continuous explanatory variables,…
Study robust optimization for discrete strategies under uncertain conditions.
problem Optimizing decisions in uncertain environments with discrete strategies.
method Nonconcave robust optimization with discrete constraints.
result Existence of maximizers under specific conditions.
New groups found with critical exponents close to but less than max.
problem Finding discrete isometry groups with critical exponents near maximum.
method Analyzing complex hyperbolic spaces to construct groups.
result Discrete isometry groups with critical exponents arbitrarily close to max but less.
Open problem: Establishing bounds for Cayley-table completion to discover discrete algorithmic axioms.
problem Discovering discrete algorithmic axioms missing in deep learning.
method Cayley-table completion as a testbed for algorithmic complexity minimization.
result Formal exact recovery bounds for Cayley-table completion.
Study error bounds in evaluating distributional computational graphs.
problem Error analysis in evaluating graphs with inputs as probability distributions.
method Establish non-asymptotic error bounds using Wasserstein-1 distance.
result Non-asymptotic error bounds for discretization errors in distributional computational graphs.
Extends Morse-Forman theory to vector-valued functions for multiparameter persistence.
problem Computing multiparameter persistence with new tools and methods.
method Adapting Forman's theory to vectorial setting and using combinatorial topological dynamics.
result Established more general result for sublevel sets and found a way to induce Morse decomposition.
Optimal regret achieved in stochastic, discrete multi-armed bandits using information-theoretic exploration.
problem Optimal exploration vs. exploitation in stochastic, discrete multi-armed bandits.
method Proposes an information-theoretic strategy based on the value of information criterion, using simulated-annealing-like updates of a parameter.
result Achieves logarithmic optimal regret with respect to the number of episodes.
MAC improves reinforcement learning by estimating action values directly.
problem Discrete-action continuous-state reinforcement learning variance reduction.
method MAC uses the agent's action value representation to estimate policy gradient, reducing variance.
result MAC reduces policy gradient variance compared to traditional methods.
Deep switch networks generate discrete data and language.
problem Generating high-dimensional discrete data and natural language.
method Adaptive switches model conditional distributions of discrete random variables. Maximum-likelihood objective function training with stochastic gradient descent.
result Stable and interpretable training of deep networks without backpropagation.
This paper investigates methods for quantifying similarity between audio signals, specifically for the task of of cover song detection. We consider an information-theoretic approach, where we compute pairwise measures of predictability between time series. We compare discrete-valued approaches operating on quantised au…
Graph neural nets improve discrete choice modeling with network effects.
problem Modeling network effects in discrete choice problems.
method Graph Convolutional Neural Network (GCNN) architecture.
result Higher predictive performance than standard models with interpretability.
New insights into RL efficiency from managing time discretization.
problem The impact of time discretization on RL methods in continuous-time systems.
method Analysis of Monte-Carlo policy evaluation for LQR systems.
result An optimal choice of temporal resolution for a given data budget improves policy evaluation efficiency.
Paper solves non-Markovian optimal stopping problems using discrete approximations.
problem Non-Markovian optimal stopping problems in continuous-time processes.
method Discrete-type approximation scheme based on variational inequalities.
result Constructs ε-optimal stopping times and optimal values in full generality.
RAD approach models both continuous and discrete data.
problem Flow models struggle with discrete structures in data.
method Domain partitioning with locally invertible functions for real and discrete latent variables.
result RAD approach models both continuous and discrete structures.
In this paper we introduce a discrete integrable system generalizing the discrete (real) cross-ratio system in S4 to complex values of a generalized cross-ratio by considering S4 as a real section of the complex Plücker quadric, realized as the space of two-spheres in S4. We develop the geometry of the Plücker…
New Y-systems for Miquel dynamics are Möbius invariant.
problem Miquel dynamics circle centers are not Möbius invariant.
method Introduced new Y-systems involving only intersection points.
result New Y-systems are Möbius invariant and satisfy the transformation group principle.
Derives an approximation algorithm for continuous submodular maximization without derivative information.
problem Maximizing a continuous submodular function with only function values and no derivative information.
method Black-box Continuous Greedy algorithm for DR-submodular functions, extended to stochastic setting.
result Achieves a (1−1/e)OPT−ε approximation guarantee with O(d/ε3) function evaluations.