Study finds formulas for minimal submanifolds using Möbius transformations.
problem Understanding minimal submanifolds in Euclidean space.
method Monotonicity formulas for minimal submanifolds involving Möbius transformations.
result Proved formulas for minimal submanifolds under Möbius transformations.
The paper proves a transformation theorem under a monotone property of almost Euclidean factors of geodesic balls.
problem The non-increasing property of numbers of almost Euclidean factors of geodesic balls.
method Proves a transformation theorem under a non-decreasing property compared to the non-increasing property.
result Shows that for a manifold with nonnegative Ricci curvature, if its universal cover is polar at infinity and the number of almost Euclidean factors is monotone, then its fundamental group is finitely generated and virtually abelian.
Efficient algorithms find optimal monotone transforms for calibration under strictly convex losses.
problem Calibrating estimations to improve performance with monotone transforms.
method Proposed linear-time and space algorithm for finding optimal monotone transforms for specific loss functions. Also proposed an anytime algorithm with linear space and pseudo-linearithmic time complexity.
result Optimal monotone transforms are unique and can be found efficiently for various strictly convex loss functions.
UMNNs improve density estimation and variational inference without constraints.
problem Creating expressive invertible transformations without constraints.
method Proposed UMNN architecture enforcing monotonicity with a free-form neural network.
result UMNNs enhance autoregressive flows for density estimation and variational inference.
CMTRF improves recommendation accuracy by transforming rating scales.
problem Non-linear transformation of rating scales disrupts low-rank structure in rating matrices.
method CMTRF performs regression up to unknown monotonic transforms over user segments, coupled with matrix factorization.
result CMTRF outperforms other baselines in synthetic and real-world datasets.
New method calibrates neural network predictions for better reliability.
problem Improper probability estimates from deep networks leading to unreliable predictions.
method Proposes a constrained optimization approach for a monotonic calibration map.
result Achieves state-of-the-art performance across various datasets and models.
Study solves optimal portfolio selection using HJB equation.
problem Optimal portfolio selection problem.
method Maximal monotone operator method, Banach fixed-point theorem, Fourier transform, monotone operators technique.
result Existence and uniqueness of solution to HJB equation.
New risk measure extensions preserve key properties.
problem Extending risk measures to larger spaces while preserving properties.
method Unique extension of dilatation monotone risk measures to L 1 L^1 L 1 . result Risk measures extend uniquely and preserve monotonicity, convexity, and cash-additivity.
The study examines distortion in specific homeomorphisms of Cantor sets.
problem Distortion in homeomorphisms of Cantor sets.
method Analyzes equivalence of conditions related to discontinuities and conjugacy.
result Elements are distorted if they satisfy certain conditions.
New method for optimizing risk in financial models using Fourier transforms.
problem Optimizing risk in financial models with multi-period mean-CVaR.
method Strictly monotone 2D integration scheme via Fourier-trained transition kernels.
result Established robust and accurate optimization method for financial models.
A new algorithm for generalized multivariate regression with monotonic responses.
problem Generalized multivariate regression with monotonic responses.
method Semi-parametric order-based algorithm maximizing rank correlation.
result The algorithm is a consistent estimator with a convergence rate of o ( 1 / n ) o(1/\sqrt{n}) o ( 1/ n ) . The paper solves a complex financial optimization problem using a novel mathematical technique.
problem Optimizing portfolio selection in financial markets.
method Maximal monotone operator method and Riccati transformation.
result Existence and uniqueness of a solution to the transformed parabolic equation in a Sobolev space.
Developed a monotone numerical method for MV portfolio optimization under jump-diffusion models.
problem Efficiently optimizing portfolios with jump-diffusion dynamics and investment constraints.
method Strictly monotone numerical integration method using Fourier transforms and composite quadrature rules.
result Proven to be ℓ ∞ \ell_{\infty} ℓ ∞ -stable and pointwise consistent, converging to the MV optimization solution. Two new algorithms solve high-dimensional optimization problems without gradients.
problem Optimizing complex, high-dimensional functions without gradient information.
method GradientLess Descent (GLD) algorithms that use evaluations at adaptively chosen inputs.
result Converges within an ε-ball of the optimum with a number of evaluations that is poly-logarithmic in dimensionality.
Decision tree predictions improve with better split point interpolation methods.
problem Interpolation errors in decision tree models can lead to misclassification.
method Comparing alternative split point interpolation methods and quantile transformation.
result Quantile transformation reduces interpolation error by up to half.
The paper tackles matrix completion under nonlinear distortions.
problem Matrix completion with nonlinear distortions.
method Alternates between low-rank matrix estimation and monotonic function estimation.
result Empirical results show the method's competitiveness.
This paper introduces a novel monotone curve estimation framework based on convex duality.
problem Estimating smooth, continuous, and monotonic curves in data.
method Convex duality and optimal transport theories.
result Established statistical guarantees for monotone curve estimates.
Paper tackles stochastic k k k -submodular bandits with full feedback, achieving sublinear regret.
problem Online optimization of k k k -submodular functions with full-bandit feedback. method Proposes online algorithms for various k k k -submodular stochastic combinatorial multi-armed bandit problems. result Achieves sublinear α α α -regret bounds for multiple k k k -submodular stochastic combinatorial multi-armed bandit problems. Combines regularization and optimal scaling for better regression models.
problem Improving regression models with categorical and continuous data.
method Integrates optimal scaling and regularization methods.
result Enhances model performance and condition of predictor correlation matrix.
This paper introduces a novel approach for learning to rank (LETOR) based on the notion of monotone retargeting. It involves minimizing a divergence between all monotonic increasing transformations of the training scores and a parameterized prediction function. The minimization is both over the transformations as well …
SLIMs hybridize sparse linear and isotonic models for high-dimensional data.
problem High-dimensional data with non-linear relationships.
method Hybridizing sparse linear models and isotonic models, proposing a two-step algorithm for estimation.
result The algorithm accurately estimates sparse parameters and monotone functions.
New kernels model non-stationary data efficiently.
problem Efficiently modeling non-stationary data with Gaussian processes.
method Model spectral density as a mixture of frequency surfaces, solve generalised Fourier transform.
result Derives efficient inference methods for non-stationary kernels.
Paper proposes an online speech recognition model using Transformer.
problem Challenges in deploying Transformer-based E2E ASR for online speech recognition.
method Chunk self-attention encoder (chunk-SAE) and monotonic truncated attention (MTA) based self-attention decoder (SAD).
result Achieved 23.66% CER with 320 ms latency, significant improvement over offline models.
New method makes CP intervals locally adaptive using trainable transformations.
problem Making Conformal Prediction intervals locally adaptive.
method Defining a trainable change of variables φ X ( A ) φ_X(A) φ X ( A ) that depends on object attributes X X X . result Locally adaptive prediction intervals with guaranteed marginal validity and variable sizes.
New framework for learning KR maps from data, ensuring stable generalization.
problem Learning monotone triangular transport maps efficiently and accurately.
method General framework using invertible transformations of smooth functions, ensuring no spurious local minima.
result Unique global minimizer corresponds to the KR map under certain conditions.
Proves flows of two-convex Lagrangians are regular, global, and converge.
problem Proves regularity, global existence, and convergence of Lagrangian mean curvature flows in the two-convex case.
method Uses a newly discovered monotone quantity to control two-convexity.
result Proves results for the mean curvature flow of area-decreasing Lagrangian submanifolds.
Study non-monotonic loss functions in CRC, achieving valid risk control with large calibration samples.
problem Non-monotonic loss functions in CRC, violating existing theory's monotonicity assumption.
method Finite grid selection, calibration sample size analysis, Lipschitz continuity, monotonicity, distribution shift.
result Valid CRC achieved with large calibration samples, optimal excess risk rate of log ( m ) / n \sqrt{\log(m)/n} log ( m ) / n . A new method solves complex financial equations efficiently.
problem Solving worst-case and best-case prices for two-factor uncertain volatility models.
method Decompose and integrate, then optimize; piecewise constant control; closed-form Green's functions; 2D convolution integrals; monotone numerical integration; Fast Fourier Transforms.
result The method efficiently computes the value function and optimal control, converging to the viscosity solution of the HJB equation.
New analysis reveals multi-branched multifractality in time series.
problem Analyzing non-monotonic behavior in mean inter-event times.
method Modified Multifractal Detrended Fluctuation Analysis with Legendre-Fenchel transform.
result Discovery of multi-branched multifractality leading to phase transitions.
Monotonicity of normalized implied-volatility coordinates under no-arbitrage
problem Monotonicity of normalized implied-volatility coordinates under no-arbitrage
method Elementary discrete no-arbitrage proof
result Monotonicity principle extended to Bachelier implied volatility
We show that the volume of a simple Riemannian metric on D n D^n D n is locally monotone with respect to its boundary distance function. Namely if g g g is a simple metric on D n D^n D n and g ′ g' g ′ is sufficiently close to g g g and induces boundary distances greater or equal to those of g g g , then v o l ( D n , g ′ ) ≥ v o l ( D n , g ) vol(D^n,g')\ge vol(D^n,g) v o l ( D n , g ′ ) ≥ v o l ( D n , g ) . Furthermor…
Neural spline flows enhance flow models with rational-quadratic splines.
problem Improving flexibility and density estimation in flow models.
method Proposes a new differentiable module based on monotonic rational-quadratic splines.
result Demonstrates improved performance in density estimation, variational inference, and generative modeling of images.
Algorithm explains XGBoost models using LIME and ILP.
problem Explain XGBoost model behavior using logic programs.
method Use LIME to select features, then apply LIME-FOLD heuristic ILP to learn non-monotonic logic programs.
result Significant improvement in classification metrics with fewer rules.
Paper uses deep learning for accurate, monotonic cardinality estimation.
problem Accurate and monotonic cardinality estimation for similarity selection.
method Feature extraction to Hamming space, followed by deep learning regression.
result Demonstrates improved query optimizer performance.
We simplify neural networks to 3D to study their topological changes.
problem Understanding how neural network layers affect low-dimensional topological invariants.
method Limiting each layer to a width of 3D space, tracking changes in linking numbers.
result ResNets and transformers are equally powerful in changing linking numbers.
SISR improves feature attribution in complex payoff schemes.
problem Distorted feature attributions due to non-additive payoff functions and high-dimensional feature spaces.
method Sparse Isotonic Shapley Regression (SISR) learns a monotonic transformation to restore additivity and enforces L0 sparsity.
result SISR achieves strong support recovery and stable attributions across various payoff schemes.
Insider trading is reduced when penalized, affecting expected penalties in a non-monotone way.
problem Reducing insider trading behavior when insiders face legal penalties.
method Characterized via a backward stochastic differential equation (BSDE) with a non-linear operator.
result The insider's expected penalties are non-monotone in the fee structure and determined by relative entropy.
New analysis of annealing paths in sampling and estimation.
problem Sampling from complex distributions and estimating normalization constants.
method Extending known results on Bregman divergence to quasi-arithmetic means under monotonic embedding.
result Analogous result for quasi-arithmetic means, highlighting the interplay between means, parametric families, and divergence functionals.
We analyze a simple asset transfer model in which the transfer amount is a fixed fraction f f f of the giver's wealth. The model is analyzed in a new way by Laplace transforming the master equation, solving it analytically and numerically for the steady-state distribution, and exploring the solutions for various values o…
TDX predicts evolving distributions from streaming data.
problem Predicting density at future time points in evolving data.
method Dynamic basis expansion with isometric log-ratio transformation.
result TDX accurately captures monotonous drift patterns.
Develops a new option pricing model under G-expectation framework.
problem Modeling uncertainty in financial markets and robust valuation under model uncertainty.
method G-expectation framework, logarithmic transformation, finite difference schemes.
result Unified risk-neutral valuation approach yielding G-Black-Scholes equation.
New Hermite approximations accelerate convergence with adaptive coordinate transformations.
problem Accelerating convergence of spectral approximations for Hermite expansions.
method Using normalizing flows for adaptive coordinate transformations and deriving error estimates.
result Error estimates for Hermite expansions under adaptive coordinate transformations.
Cubic-Spline Flows improve autoregressive flow performance in density estimation.
problem Improving the performance of flow-based models in density estimation.
method Stacking a new coupling transform based on monotonic cubic splines with LU-decomposed linear layers.
result Cubic-Spline Flows close the gap with autoregressive flows on density-estimation tasks.
A novel approach finds optimal compromise solutions in many-objective Bayesian optimization.
problem Extending multiobjective Bayesian optimization to many objectives.
method Kalai-Smorodinski solution in copula space, tailored Bayesian optimization algorithm.
result The Kalai-Smorodinski solution is found to be interpretable and insensitive to objective transformations.
Polynomial bound on tightening curves on surfaces without increasing crossings.
problem Proving a polynomial bound on the number of monotonic homotopy moves for curves on surfaces.
method Combining tools from hyperbolic geometry and graph drawing algorithms.
result First polynomial bound on the number of monotonic homotopy moves, improving from exponential.
Introduces nondecreasing rank for matrices and tensors, developing methods and applications.
problem Finding low-rank approximations for matrices and tensors with monotonic constraints.
method Developed a variant of hierarchical alternating least squares algorithm for finding low ND rank approximations.
result Low ND rank factorizations can be found and interpreted for real-world datasets.
We present new extensions to a method for constructing several families of solvable one-dimensional time-homogeneous diffusions whose transition densities are obtainable in analytically closed-form. Our approach is based on a dual application of the so-called diffusion canonical transformation method that combines smoo…
The aim of this paper is to construct and analyze solutions to a class of Hamilton-Jacobi-Bellman equations with range bounds on the optimal response variable. Using the Riccati transformation we derive and analyze a fully nonlinear parabolic partial differential equation for the optimal response function. We construct…