Quantum channels' contraction under privacy constraints studied.
problem Understanding the privacy constraints on quantum channel contractions.
method Established upper bounds on contraction coefficients for specific divergences under QLDP constraints.
result Upper bounds and full characterization of contraction coefficients for specific quantum distances.
Study optimal consumption and investment strategies with constraints in a market with random coefficients.
problem Optimal consumption and investment strategies with constraints in a regime switching market with random coefficients.
method Explicit optimal strategies provided via solutions to new BSDE systems.
result Solving new BSDEs to find optimal values and strategies.
The paper tackles online resource allocation with uncertain coefficients and chance constraints.
problem Online stochastic resource allocation problem with chance constraints.
method Linearization and primal-dual algorithms with heuristic corrections.
result Optimality gap and constraint violation are on the order of √n.
We investigate the ergodic problem of growth-rate maximization under a class of risk constraints in the context of incomplete, Itô-process models of financial markets with random ergodic coefficients. Including {\em value-at-risk} (VaR), {\em tail-value-at-risk} (TVaR), and {\em limited expected loss} (LEL), these cons…
We extend Donaldson's diagonalization theorem to intersection forms with certain local coefficients, under some constraints. This provides new examples of non-smoothable topological 4-manifolds.
New method improves DAG learning by using large coefficients for higher-order terms.
problem Recovering DAG structures from observational data is challenging due to combinatorial optimization.
method Proposes truncated matrix power iteration to approximate DAG constraints efficiently.
result Empirically outperforms previous methods by a factor of 3 or more in structural Hamming distance.
Analytic networks with bounded coefficients can't outperform polynomial approximations.
problem Approximation limits of neural networks with analytic activation functions under coefficient constraints.
method Deterministic analysis using comparison argument and Bernstein-type estimates.
result Networks with analytic activation functions and controlled coefficients cannot outperform classical polynomial approximation rates on non-analytic targets.
Study optimal investment-reinsurance strategy for insurers under random coefficients and jumps.
problem Optimal investment-reinsurance strategy for insurers with random coefficients and jumps.
method Solves backward stochastic differential equations with jumps under a convex cone constraint.
result Optimal strategy and value remain the same even with random coefficients and jumps.
We consider stationary autoregressive processes with coefficients restricted to an ellipsoid, which includes autoregressive processes with absolutely summable coefficients. We provide consistency results under different norms for the estimation of such processes using constrained and penalized estimators. As an applica…
Extends compactness theory to variable-coefficient pseudo-differential operators on manifolds.
problem Compensated compactness for pseudodifferential operators on vector bundles.
method Establishes a theorem for weakly convergent sequences of sections under a pseudo-differential operator.
result Quadratic form converges in distributional sense under certain conditions.
Study algebraic invariants from lightning self-attention models.
problem Understanding polynomial coefficients of self-attention mechanisms.
method Identify algebraic invariants using polynomial coefficients and coordinate geometry.
result Found linear and nonlinear families of algebraic invariants.
The non-negative solution to an underdetermined linear system can be uniquely recovered sometimes, even without imposing any additional sparsity constraints. In this paper, we derive conditions under which a unique non-negative solution for such a system can exist, based on the theory of polytopes. Furthermore, we deve…
The paper solves MMV and MV problems with random coefficients and finds shared optimal strategies.
problem Optimal trading strategies with random market coefficients.
method Backward stochastic differential equations (BSDEs) to find optimal strategies.
result MMV and MV problems share the same optimal portfolio and value under random coefficients.
We develop a highly scalable optimization method called "hierarchical group-thresholding" for solving a multi-task regression model with complex structured sparsity constraints on both input and output spaces. Despite the recent emergence of several efficient optimization algorithms for tackling complex sparsity-induci…
Classifies links with small Khovanov homology ranks.
problem Classifying links with specific ranks in Khovanov homology.
method Previous results combined with new classifications.
result All links with ranks ≤ 8 and three-component links with ranks ≤ 12 are classified.
Multi-view clustering is an important and fundamental problem. Many multi-view subspace clustering methods have been proposed, and most of them assume that all views share a same coefficient matrix. However, the underlying information of multi-view data are not fully exploited under this assumption, since the coefficie…
We consider regression scenarios where it is natural to impose an order constraint on the coefficients. We propose an order-constrained version of L1-regularized regression for this problem, and show how to solve it efficiently using the well-known Pool Adjacent Violators Algorithm as its proximal operator. The main ap…
The modified Korteweg-de Vries hierarchy (mKdV) is derived by imposing isometry and isoenergy conditions on a moduli space of plane loops. The conditions are compared to the constraints that define Euler's elastica. Moreover, the conditions are shown to be constraints on the curvature and other invariants of the loops …
Study on spherical CR manifolds with non-trivial Chern classes.
problem Understanding Chern classes in spherical CR manifolds.
method Construction and proof of constraints on Chern classes.
result Topological obstruction to spherical CR structures on contact manifolds.
Investor optimizes investment and consumption under uncertain market conditions with constraints.
problem Investor optimizes investment and consumption in a stochastic environment with model uncertainty and constraints.
method Robust control problem solved using stochastic Hamilton-Jacobi-Bellman-Isaacs equations, backward stochastic differential equations, and bounded mean oscillation martingale theory.
result Investor incurs utility loss when ignoring model uncertainty, and constraints impact optimal strategy and value function.
The performance of Orthogonal Matching Pursuit (OMP) for variable selection is analyzed for random designs. When contrasted with the deterministic case, since the performance is here measured after averaging over the distribution of the design matrix, one can have far less stringent sparsity constraints on the coeffici…
c-lasso is a Python tool for robust and sparse regression with linear constraints.
problem Sparse and robust linear regression with linear constraints.
method Estimates coefficients and scale under linear constraints using perspective M-estimators.
result Provides estimators for various loss functions with linear constraints.
New MMM captures hierarchical marketing effects and sign restrictions.
problem Measuring effectiveness of marketing activities with hierarchical structure and sign constraints.
method Proposes a constrained maximum likelihood approach using Hamiltonian Monte Carlo algorithm.
result Demonstrates superior performance on real datasets compared to multi-stage methods.
This paper establishes the existence of a unique nonnegative continuous viscosity solution to the HJB equation associated with a Markovian linear-quadratic control problems with singular terminal state constraint and possibly unbounded cost coefficients. The existence result is based on a novel comparison principle for…
New techniques solve Riccati equations on 3D manifolds, finding 4th order metric obstructions.
problem Solving Riccati-type equations with algebraic constraints on 3D Riemannian manifolds.
method Real algebraic geometry techniques, focusing on connection coefficients and Hessian equations.
result Obstruction to solving Riccati equations has order 4 in metric coefficients.
Paper extends LME models to allow sign constraints on coefficients with SDTN random effects.
problem Inference with sign constraints on random effects in LME models.
method Proposes SDTN distribution for random effects and develops likelihood-based approaches for estimation.
result Proposed constrained model improves real-world interpretations and achieves satisfactory performance.
Study on harmonic maps from surfaces to homogeneous spaces, focusing on bubble formation and geometric constraints.
problem Understanding the behavior of harmonic maps from surfaces to homogeneous spaces, especially in the presence of bubbles.
method Refined asymptotic expansions and obstruction relations for sequences developing a single bubble, geometric constraints for weakly conformal maps.
result New geometric constraints on the tangent planes of the limit map and bubble, depending on the dimensionality.
This work studies the contraction coefficients of Schrödinger bridge problems in linear systems.
problem Optimally controlling the evolution of a system's state density over time.
method Analyzes and improves the convergence rates of dynamic Schrödinger systems via geometric and control-theoretic interpretations.
result New insights into improving computation of worst-case contraction coefficients by preconditioning.
ARO overfits by making constraints dependent on uncertainty, leading to brittleness.
problem ARO's adaptive policies become brittle when realizations fall outside the uncertainty set.
method Assigning constraint-specific uncertainty set sizes with probabilistic guarantees.
result Regularization through specific uncertainty set sizes ensures stability and flexibility.
New proof of Alexander polynomial constraints for lens space surgeries.
problem Constraints on Alexander polynomials for lens space surgeries.
method Using changemaker lattices to prove a theorem.
result Constraints on Alexander polynomials for specific surgeries.
Study S-shaped utility maximization with VaR constraint and unobservable drift.
problem Maximizing utility with a Value at Risk (VaR) constraint and unknown drift.
method Bayesian filter, concavification principle, change of measure, semi-closed integral representation, algorithms (Lagrange, simulation, deep neural network).
result Critical wealth level determining solution feasibility and optimal solution existence.
Paper solves complex game theory problems with new equations.
problem Zero-sum stochastic games with non-Markovian switching.
method New multidimensional SRE and BSDE solutions.
result Existence and uniqueness of SRE solutions.
Study knots with genus one, finds Gordian distance and cosmetic crossing constraints.
problem Understanding knots with genus one and their properties.
method Using HOMFLT polynomials to find obstructions for Gordian distance and cosmetic crossings.
result Proves the (generalized) cosmetic crossing conjecture for genus one pretzel knots.
We consider {\em Mixed Linear Regression (MLR)}, where training data have been generated from a mixture of distinct linear models (or clusters) and we seek to identify the corresponding coefficient vectors. We introduce a {\em Mixed Integer Programming (MIP)} formulation for MLR subject to regularization constraints on…
Study consumption-investment problem in markets with rank-based returns.
problem Consumption-investment problem in markets with rank-based returns.
method Derives an HJB equation with Neumann boundary conditions for the value function and proves a corresponding verification theorem.
result Explicit solutions for unconstrained, open market constraints, and fully invested cases.
Proposes an adversarial algorithm to learn unbiased representations via HGR coefficient.
problem Learning fair representations without sensitive attribute information.
method Adversarial algorithm using Hirschfeld-Gebelein-Renyi (HGR) maximal correlation coefficient.
result Significant improvements in bias mitigation compared to existing methods.
LDP is equivalent to contraction of E_γ-divergence, impacting privacy and utility.
problem Analyzing trade-offs between privacy and utility in estimation problems.
method Equivalence of LDP constraints to contraction coefficients of E_γ-divergence, using f-divergences and estimation-theoretic tools.
result LDP guarantees can be expressed in terms of contraction coefficients of arbitrary f-divergences.
DS2CF-Net learns hierarchical representations with deep coupled factorization and enriched prior.
problem Learning deep hierarchical representations from data.
method Dual-constrained Deep Semi-Supervised Coupled Factorization Network (DS2CF-Net) with enriched prior.
result DS2CF-Net achieves state-of-the-art performance in representation learning and clustering.
Study shows global invertibility in nonlinear elasticity with vanishing self-repulsion term.
problem Global invertibility in nonlinear elasticity with a vanishing nonlocal self-repulsion term.
method Proves global invertibility in the Γ-limit of elastic energy with a vanishing nonlocal self-repulsion term. result Global invertibility can be obtained in the Γ-limit of the elastic energy with a vanishing nonlocal self-repulsion term. Sharp fractional Sobolev inequalities on closed manifolds identified.
problem Critical fractional Sobolev embedding on closed Riemannian manifolds.
method Intrinsic heat-kernel based framework, determining optimal coefficients, proving sharp inequalities.
result Sharp p-power inequality and almost sharp inequality established. A new framework for information theory considers computational constraints.
problem Understanding information in complex systems with computational limitations.
method Variational extension of Shannon's information theory with computational constraints.
result Predictive V-information can be created through computation and reliably estimated from data. Solves optimal stopping problem with Poisson constraints using jumps.
problem Optimal stopping with Poisson constraints and jumps.
method Penalized backward stochastic differential equation (PBSDE) with jumps, decomposition method based on Jacod-Pham, comparison theorem of BSDEs with jumps.
result Solves American option pricing in nonlinear markets with Poisson constraints.
We consider a semilinear parabolic degenerated Hamilton-Jacobi-Bellman (HJB) equation with singularity which is related to a stochastic control problem with fuel constraint. The fuel constraint translates into a singular initial condition for the HJB equation. We first propose a transformation based on a change of vari…
We derive an explicit formula for likelihood function for Gaussian VARMA model conditioned on initial observables where the moving-average (MA) coefficients are scalar. For fixed MA coefficients the likelihood function is optimized in the autoregressive variables Φ's by a closed form formula generalizing regression c…
Decomposes bias in linear models under demographic parity constraints.
problem Understanding and quantifying bias in linear models under fairness constraints.
method Post-processing framework to decompose bias into direct and indirect components.
result Analytical characterization of how demographic parity reshapes model coefficients.
New algorithm solves utility maximization with deep learning for constrained problems.
problem Maximizing utility under convex constraints with random coefficients.
method Developed a new algorithm using stochastic maximum principle and deep learning.
result The new algorithm outperforms existing methods in accuracy and applicability.
The paper derives statistics of multi-factor functions from their Fourier transforms.
problem Deriving statistics of multi-factor functions from Fourier transforms.
method Developed an m-Coefficient/Index Annihilation Theorem to analyze the moments of a function from its Fourier transform.
result The mth moment of a function becomes a series of terms, each with precisely m Fourier coefficients, and the indices sum to zero.
Motivated by the problem of optimal portfolio liquidation under transient price impact, we study the minimization of energy functionals with completely monotone displacement kernel under an integral constraint. The corresponding minimizers can be characterized by Fredholm integral equations of the second type with cons…