XOFM explains attribute effects in ordinal regression using piece-wise linear functions.
problem Lack of detailed attribute contributions in existing ordinal regression models.
method XOFM uses piece-wise linear functions to approximate attribute contributions and introduces ordinal transformation.
result XOFM provides superior explainability and state-of-the-art prediction accuracy.
LS-PLM predicts ad clicks from large scale sparse data.
problem Predicting click-through rates (CTR) from large scale nonlinear sparse data.
method Formulated with L1 and L2,1 regularizers, solved with directional derivatives and quasi-Newton method, and distributed on hundreds of machines. result Captures nonlinear patterns from massive sparse data, reducing feature engineering.
L*ReLU improves deep learning for fine-grained image classification.
problem Fine-grained image classification requires specific AFs.
method Proposes L*ReLU, piece-wise linear AFs for deep learning.
result L*ReLU achieves superior results on FGVC datasets.
DAMI uses interpretable regions to select informative samples for deep learning models.
problem Efficiently identifying informative samples for deep learning models with minimal annotation cost.
method Inspired by piece-wise linear interpretability in DNN, DAMI selects samples on different linearly separable regions.
result DAMI outperforms state-of-the-art approaches in tabular data.
RUMBoost combines RUMs and deep learning for better choice modelling.
problem Creating interpretable and robust discrete choice models.
method Gradient Boosted Regression Trees for utility functions, with constraints for interpretability and monotonicity.
result RUMBoost outperforms ML and RUM benchmarks in predictive performance and interpretability.
We introduce a new activation function using Chebyshev-Lagrange polynomials for improved neural network performance.
problem Improving data efficiency and accuracy of neural networks.
method Parameterized piece-wise polynomial activation functions based on Chebyshev nodes and Lagrangian interpolation.
result Significant improvements in model capacity and accuracy, especially in linear extrapolation.
Researchers solve a complex financial control problem with explicit policies.
problem Constrained LQ control with multiplicative noise in financial risk management.
method Derived analytical control policy using state separation property and solving coupled Riccati equations.
result Explicit piece-wise affine control policy for optimal control of stochastic systems.
Deep nets' optima are surprisingly connected by simple paths.
problem Understanding the loss landscape of deep nets.
method Mathematical explanations based on generic properties of well-trained nets.
result Optima in deep nets are connected by piece-wise linear paths.
Estimates change-points and graph structures in a time-varying Ising model.
problem Detecting and understanding changes in a time-varying Ising model.
method Maximizing a penalized conditional log-likelihood to estimate neighborhood of each node, enforcing sparsity and piece-wise constant graph structures.
result First change-points consistency theorems for unknown number of change-points in time-varying Ising model.
PyChEst detects changes in non-stationary time series without distributional assumptions.
problem Detecting changes in non-stationary time series data.
method Nonparametric algorithms for consistent detection of multiple changepoints in piece-wise stationary processes.
result PyChEst consistently detects changes without distributional assumptions.
This paper proposes a method to approximate non-Gaussian likelihoods in Gaussian Processes.
problem Approximating non-Gaussian likelihoods in Gaussian Processes.
method Proposes a piece-wise constant approximation for the inverse-link function.
result Yields a closed form solution for the SVGP lower bound.
Neural models can realize decision trees with parameter sharing and improved performance.
problem Training and optimizing oblique decision trees.
method Locally constant networks based on ReLU gradients, parameter sharing, and neural tools.
result Locally constant networks can implicitly model oblique decision trees with fewer neurons.
A new algorithm finds optimal solutions for constrained decision processes.
problem Optimizing state-value functions with constraints in CMDPs.
method Gradient-Aware Search (GAS) exploiting PWLC structure.
result GAS converges faster and more reliably than existing methods.
The paper introduces robustness certificates for ReLU networks to protect against adversarial perturbations.
problem The vulnerability of ReLU networks to small adversarial perturbations.
method The paper proposes two lower bounds for the distance of a given input sample to the classification decision boundary of a ReLU network.
result The proposed simplex certificate is a closed-form, differentiable, and computationally efficient robustness measure.
Survey on heat kernels and path integrals.
problem Approximating Wiener measure on compact manifolds.
method Review of recent results on approximating Wiener measure.
result Approximation of Wiener measure by measures on spaces of piece-wise geodesics.
Bayesian method detects change points and clusters in piece-wise constant signals.
problem Detecting change points and clustering in piece-wise constant signals.
method Nonparametric penalized least square model selection on partitions of design points, with an efficient algorithm.
result Oracle inequality and adaptive upper bound on expected square risk of the estimator.
Method to create rational Seifert surfaces for knots in Lens space.
problem Creating rational Seifert surfaces for knots in Lens space.
method Assuming a regular projection, construct rational Seifert surface on twist toroidal diagram.
result A method to construct rational Seifert surfaces for knots in Lens space.
Let S be a triangulated 2-sphere with fixed triangulation T. We apply the methods of thin position from knot theory to obtain a simple version of the three geodesics theorem for the 2-sphere [5]. In general these three geodesics may be unstable, corresponding, for example, to the three equators of an ellipsoid. Using a…
Solves optimal control with constraints for stochastic systems.
problem Optimal control of constrained stochastic linear-quadratic systems.
method State separation theorem and Riccati equations for explicit solution.
result Explicit piecewise affine optimal control policy.
This paper proposes a distributed Bayesian method for piecewise sparse linear models.
problem High computational cost in simultaneous model selection for piecewise linear models.
method Distributed factorized asymptotic Bayesian (FAB) inference on distributed memory architectures.
result Achieves high prediction accuracy and performance scalability.
Discrete approach proves a new version of Wirtinger's inequality.
problem Classical Wirtinger's inequality for piece-wise functions.
method Theorem of classification of isometries and Fourier series development.
result New elementary proof of Wirtinger's inequality.
New methods for calculating curvature in graph theory.
problem Calculating curvature in graphs and random walks.
method Analyzing continuous and discrete-time Ollivier-Ricci curvatures of weighted graphs.
result Generalized existence and properties of Ollivier-Ricci curvature for various random walks.
Optimal order execution strategies for brokers under reference benchmarks.
problem Maximizing broker's utility of excess profit-and-loss subject to reference strategies.
method Formulated as a utility maximization problem, optimal strategies derived in closed form.
result General reference strategies can be approximated by piece-wise linear combinations of IS and TC orders.
Efficiently infers switching nonlinear systems with collapsed amortized variational inference.
problem Inference in switching nonlinear dynamical systems with discrete latent variables.
method Learn an inference network as a proposal for continuous latent variables, performing exact marginalization of discrete variables.
result Successfully segments time series data into meaningful regimes using piece-wise nonlinear dynamics.
We propose a strategy for approximating Pareto optimal sets based on the global analysis framework proposed by Smale (Dynamical systems, New York, 1973, pp. 531-544). The method highlights and exploits the underlying manifold structure of the Pareto sets, approximating Pareto optima by means of simplicial complexes. Th…
This work simplifies adversarial attacks using neural networks, reducing computation and improving training convergence.
problem Efficiently generating and training against ideal adversarial attacks with minimal computational overhead.
method Representing ideal adversarial attacks as smooth piece-wise functions and approximating them with neural networks. Using a mathematical game between an attack network and a defense network for adversarial training.
result Obtained convergence rates of adversarial loss in terms of sample size n for adversarial training. A new method for creating simpler models from complex ones.
problem Creating accurate approximations of complex models at reduced costs.
method Sequential adaptive surrogate modeling based on locally spectral expansions.
result Stochastic spectral embedding (SSE) shows good approximation capabilities and scalability.
Paper investigates a new type of elastica formed during beam rupture.
problem Understanding the shape of a beam during sudden rupture.
method Developed a mathematical theory using elliptic ζ-function.
result Explicit shape of the new elastica (Λ-elastica) is described.
Improved optimization methods for discrete distributions reduce bias in gradient estimation.
problem Estimating gradients for discrete distribution parameters is challenging.
method Analyzed and proposed methods to reduce bias in gradient estimation, including Gumbel-Softmax and piece-wise linear continuous relaxation.
result Reduced bias leads to better performance in variational inference and binary optimization tasks.
A new method to measure neural network expressiveness using tighter upper bounds.
problem Measuring the expressiveness of deep neural networks (DNNs).
method Proposes a new tighter upper bound for the number of linear regions in rectifier networks, using matrix computation.
result The proposed upper bound is tighter than existing ones and explains the performance improvements of skip connections and residual structures.
Paper reformulates UOT as non-negative penalized linear regression for efficient algorithms.
problem Optimal transport with relaxed marginal conditions.
method Reformulate UOT as non-negative penalized linear regression, propose multiplicative updates.
result Efficient algorithms for UOT with quadratic penalties, continuity of solutions.
Neural network discovers exact solutions to QP with linear constraints.
problem Discovering exact solutions to Quadratic Programs (QP) with linear constraints using neural networks.
method Proposes a neural network modeling approach that analytically derives model parameters from problem coefficients, ensuring closed-form solutions without training.
result The closed-form NN model produces exact solutions for every critical region of the QP solution function, outperforming DNNs and commercial solvers in terms of optimality and feasibility.
This paper extends depth separation results to piece-wise oscillatory functions.
problem Approximating functions with piece-wise oscillatory structure using neural networks.
method Extends existing results to piece-wise oscillatory functions using proof strategy from (Eldan and Shamir, 2016).
result Approximation by one-hidden-layer networks holds at a poly(d) rate for functions with constant domain radius and oscillation rate.
Neural model accelerates SDDP for stochastic optimization.
problem Exponential complexity of SDDP limits its applicability to low-dimensional problems.
method Trainable neural model maps problem instances to a low-dimensional piecewise linear value function.
result ν-SDDP significantly reduces problem solving cost without sacrificing solution quality.
New framework optimizes classification trees with logistic loss and ℓ1 regularization.
problem Improving interpretability and generalization of classification trees.
method Developed a generalized framework for CTs, incorporating logistic loss and ℓ1 regularization. result Optimal Logistic Tree model outperforms state-of-the-art MIP-based approaches in terms of interpretability and generalization.
Probabilistic solvers improve stability for stiff systems.
problem Performance penalties for small steps in stiff systems.
method Probabilistic exponential integrators that include fast linear dynamics in the prior.
result Proven L-stability and probabilistic error accounting.
Novel method converts time series data into functional data for high dimensional classification.
problem Small sample size problem in high dimensional time series data.
method Classwise Functional Principal Component Analysis (PCA) followed by Bayesian linear classifier.
result Demonstrated efficacy on synthetic and real data sets.
The paper proposes new cross-correlators using Price's Theorem and piecewise-linear decomposition.
problem Optimal method for estimating cross-correlations using finite samples.
method General mathematical framework using Price's Theorem and piecewise-linear decomposition.
result Some cross-correlators based on Huber's loss functions, MP functions, and LSE functions have higher SNR.
Most of machine learning approaches have stemmed from the application of minimizing the mean squared distance principle, based on the computationally efficient quadratic optimization methods. However, when faced with high-dimensional and noisy data, the quadratic error functionals demonstrated many weaknesses including…
Investment and insurance decisions are studied in a model with nonlinear portfolio frictions and background risk.
problem Investment and insurance decisions under a model with nonlinear portfolio frictions and background risk.
method Dynamic programming approach to find optimality conditions.
result Agent can choose to assume, partially assume, or purchase total insurance against adverse jumps in wealth.
Study improves caplet calibration for 1Y maturity using different models.
problem Calibrate 1Y caplet smile better across strike range.
method Alternative local volatility terms and stochastic volatility models.
result Some models calibrate well to 1Y caplet smile across strike range.
The paper proves Sard's theorem for polynomial maps in infinite dimensions.
problem The validity of Sard's theorem for polynomial maps in infinite-dimensional Banach manifolds.
method Sharp quantitative criteria for the validity of Sard's theorem.
result The paper provides criteria for the validity of Sard's theorem in infinite-dimensional Banach manifolds.
Proposes a method for inference in high-dimensional classification with non-differentiable surrogate losses.
problem Lack of inference procedures for identifying driving factors in high-dimensional classification with non-differentiable surrogate losses.
method Kernel-smoothed decorrelated score and cross-fitted version for hypothesis tests and interval estimators.
result Valid and superior inference methods for high-dimensional classification with non-differentiable surrogate losses.
A method for identifying NPWARX models with arbitrary domains using probabilistic mixture models.
problem Identifying hybrid system models with discontinuous maps.
method Probabilistic mixture model with a neural network for nonlinear partitioning and Expectation Maximization for parameter estimation.
result Demonstrated on a nonlinear piece-wise problem with discontinuous maps.
Paper proposes a novel SVM method for creating survival trees.
problem Creating non-linear survival trees for right-censored data.
method L2-regularized dipole splitting criteria with kernel methods.
result Non-linear splits using polynomial and Gaussian kernels show similar predictive power but often smaller tree sizes.
Self-supervised method estimates distances on fisheye cameras for autonomous driving.
problem Accurate Euclidean distance estimation on fisheye cameras for autonomous driving.
method Self-supervised scale-aware framework for monocular fisheye videos.
result State-of-the-art results on KITTI dataset, comparable to other methods.
It is shown that most of the well-known basic results for Sobolev-Slobodeckii and Bessel potential spaces, known to hold on bounded smooth domains in Rn, continue to be valid on a wide class of Riemannian manifolds with singularities and boundary, provided suitable weights, which reflect the nature of the s…
Given two points on a soup can or conical cup with lid, we find and classify all paths of minimal length connecting them. When the number of minimal paths is finite, there are at most four on a can and three on a cup. At worst, minimal paths are piece-wise smooth with three components, each of which is a classical geod…