DREAM model improves computational efficiency for non-linear effects in relational event models.
problem Efficiently modeling non-linear effects in dynamic relational networks.
method Introduces Deep Relational Event Additive Model (DREAM) using Neural Additive Models.
result Demonstrates superior computational efficiency compared to traditional REM approaches.
Bayesian non-linear matrix completion tackles large, sparse data.
problem Predict missing elements in large, sparsely observed matrices.
method Bayesian Gaussian process latent variable models with data-parallel distributed computation.
result Scalable Bayesian non-linear matrix completion outperforms linear methods.
WeSpeR speeds up non-linear shrinkage for high-dimensional weighted covariance.
problem Computing non-linear shrinkage formulas for high-dimensional weighted sample covariance.
method Derive extit{WeSpeR} algorithm using asymptotic sample spectrum properties.
result Significantly speeds up non-linear shrinkage in dimensions higher than 1000.
Learning codes for non-linear computations improves resilience in machine learning.
problem Resilience of machine learning models in the face of unavailability.
method Learning neural network architectures to design codes for non-linear computations.
result Learned codes can reconstruct up to 98% of unavailable predictions from neural networks.
Quantum computing offers a quadratic speedup for estimating non-linear functionals.
problem Estimating non-linear functionals of probability distributions.
method Proposes a quantum-inside-quantum Monte Carlo algorithm for a broad class of non-linear estimation problems.
result Achieves a quadratic speedup for non-linear estimation problems, including nested conditional expectations and stochastic optimization.
This work optimizes reservoir computing models by linking recurrence and non-linear dynamics.
problem Understanding how recurrence and non-linear dynamics in cortical networks contribute to their function.
method Transformed time-continuous, recurrent dynamics into an effective feed-forward structure of linear and non-linear temporal kernels.
result Optimal time-series classifiers can be built from random reservoir networks, demonstrating significant performance gains.
New method improves covariance estimation for weighted samples.
problem Improving covariance estimation for weighted sample data.
method Asymptotic non-linear shrinkage formulas for covariance and precision matrix estimators of weighted sample covariances.
result Asymptotic non-linear shrinkage formulas for covariance and precision matrix estimators of weighted sample covariances.
This work proposes a new algorithm for efficient reduced modeling of non-linear dynamical systems.
problem Reduced modeling of computationally demanding dynamical systems to balance accuracy and complexity.
method Embedding trajectories in a RKHS, solving low-rank constraint optimization problems, and exploiting kernel-based computations.
result The proposed algorithm achieves a gain in approximation accuracy and computational efficiency.
Paper introduces non-linearity signature to measure deep neural network performance.
problem Difficulty in explaining performance differences among similar DNN architectures.
method Affine Optimal Transport mappings to measure non-linearity.
result Signature provides better understanding of DNN inner workings.
New algorithm improves dynamic mode decomposition for high-dimensional data.
problem Reduced modeling in high-dimensional spaces.
method Low rank constraint optimization and kernel-based computation.
result Gain in approximation accuracy and computational efficiency.
New method adds all interactions in non-linear models without high computational cost.
problem Missing interactions in interpretable machine learning models.
method Additive higher-order factorization machines using tensor product splines.
result Scalable model with interactions at low computational cost.
Inference-aware meta-alignment of LLMs reduces computational cost.
problem Aligning LLMs to diverse human preferences is challenging due to conflicting criteria.
method IAMA trains a base model to be aligned to multiple tasks via different inference-time alignment algorithms, using non-linear GRPO for optimization.
result IAMA enables effective alignment of LLMs to multiple criteria with limited computational budget.
Gaussian processes emulate complex non-linear models efficiently.
problem Efficiently simulate and analyze highly non-linear, time-evolving systems.
method Gaussian process emulators to approximate model output, considering input uncertainty and time series correlation.
result High predictive performance and uncertainty measures for Lorenz and Van der Pol equations.
Efficient estimator for non-linear regression problems using convex programming.
problem Non-linear regression problems with difference of convex (DC) non-linearities.
method Formulated as a convex program, using an approximation oracle for gradients.
result Produces accurate estimates with high probability under certain assumptions.
Develops an efficient method for real-time data analysis and visualization.
problem Challenges of analyzing high-dimensional data.
method Incremental non-linear manifold approximation using GMRA framework.
result Accurately represents non-linear manifolds with small initial samples.
Unified framework for non-linear attention using modern Hopfield networks.
problem Improving transformer model's understanding of complex relationships and efficiency.
method Proposes an energy functional based on Modern Hopfield Networks (MNH) to unify linear and non-linear attention mechanisms.
result Context wells encapsulate contextual relationships among tokens, offering a richer representation of non-linear data.
Non-linear shrinkage isn't optimal for portfolio optimization, especially when asset dependence is non-stationary.
problem Optimizing portfolios with non-stationary asset dependence structures.
method Derived and compared non-linear shrinkage with an optimal target for covariance matrix estimation.
result Non-linear shrinkage can be significantly improved for portfolio optimization.
We introduce the Randomized Dependence Coefficient (RDC), a measure of non-linear dependence between random variables of arbitrary dimension based on the Hirschfeld-Gebelein-Rényi Maximum Correlation Coefficient. RDC is defined in terms of correlation of random non-linear copula projections; it is invariant with respec…
New method for interpreting non-linear models using forward marginal effects.
problem Interpreting non-linear models' feature effects is challenging.
method Introducing forward marginal effects and partitioning feature space for better interpretation.
result Improved interpretation of non-linear prediction functions.
ENIAC method optimizes and explores complex RL problems with non-linear policies.
problem Theoretical understanding of non-linear policies in RL with strategic exploration.
method ENIAC, an actor-critic method for non-linear function approximation.
result ENIAC finds near-optimal policies in polynomial exploration rounds under bounded eluder dimension.
Deep learning improves sensor performance optimization.
problem Optimizing sensor performance based on key metrics.
method Re-approach non-linear regression using deep learning with Keras and Tensorflow.
result Deep learning models improve sensor performance optimization.
This paper introduces an acceleration structure for hyperbolic embeddings.
problem Efficiently embedding and visualizing high-dimensional data in hyperbolic spaces.
method Building upon a polar quadtree, the paper introduces a new acceleration structure for hyperbolic embeddings.
result The new method computes embeddings in significantly less time compared to existing methods.
We provide a pointwise confidence bound for non-linear least-squares with fixed design.
problem Confidence estimation in non-linear ℓ 2 \ell^2 ℓ 2 -regularized least squares. method Pointwise confidence bound for local minimizers, using weighted norm involving inverse-Hessian.
result The proposed confidence bound scales with the test input's similarity to the training data.
NO-BEARS algorithm speeds up gene network inference from transcriptomic data.
problem Constructing accurate gene regulatory networks from transcriptomic data.
method NO-BEARS algorithm, based on NOTEARS, with new constraint and polynomial regression loss.
result Significantly reduced computational time and improved accuracy in inferring gene regulatory networks.
Study optimal execution in financial markets with constraints.
problem Optimal execution with non-negative constraints in a linear price impact model.
method Purely probabilistic approach via non-linear ODE.
result Complete characterization of value and optimal control.
CRCCA framework improves non-linear CCA with compressed representations.
problem Non-linear CCA for multi-view data with limited samples.
method Information-theoretic compressed representation framework (CRCCA) based on lattice quantization.
result The CRCCA framework provides theoretical bounds and optimality conditions, offering a flexible and computationally efficient solution.
PEA improves PCA and k-means for non-linear data and complex clusters.
problem Non-linear dimensionality reduction and clustering challenges.
method Principal Elliptical Analysis (PEA) for efficient non-linear approximation.
result PEA outperforms k-means in complex data clustering.
New GP model tackles physics constraints efficiently.
problem Lack of efficient, physics-informed models for complex systems.
method Physics-informed variational state-space Gaussian process.
result Efficient spatio-temporal modeling with improved performance.
Extends model uncertainty framework to non-linear affine processes for longevity bonds and contingent claims.
problem Model uncertainty and non-linear affine processes in financial markets.
method Extended reduced-form setting with affine process intensities, introduced longevity bond, and priced contingent claims.
result Consistent valuation of longevity bonds and arbitrage-free market under sublinear operator.
A systematic algorithm for building integrating factors of the form mu(x,y') or mu(y,y') for non-linear second order ODEs is presented. When such an integrating factor exists, the algorithm determines it without solving any differential equations. Examples of ODEs not having point symmetries are shown to be solvable us…
New definitions of ESP for quantum reservoir computing handle non-stationary systems.
problem Traditional ESP does not apply to non-stationary systems.
method Introduce two new categories of ESP: non-stationary ESP and subset/subspace ESP.
result Demonstrates correspondence between non-stationary ESP and QRC with NARMA tasks.
Improved Kalman filter for non-linear, non-Gaussian data.
problem Estimating hidden variables with non-linear, non-Gaussian observations.
method Reproduces and extends Burkhart et al.'s discriminative Kalman filter.
result Enhanced filter performance for complex observation models.
A fast deep learning method for parallel MRI without calibration.
problem Calibration issues in parallel MRI reconstruction.
method Model-based deep learning, self-learning non-linear annihilation filters, Fourier domain pre-learning.
result Significantly faster than SLR methods (3 orders of magnitude), improved performance with spatial domain prior.
Adversarial nets learn independent features from joint distributions.
problem Learning independent features from complex joint distributions.
method Adversarial objectives to optimize mutual information implicitly.
result Adversarial nets can solve both linear and non-linear ICA problems.
Improved RTM uses integer weights to reduce computation and increase interpretability.
problem Lack of interpretability in nonlinear regression models.
method Integer weighted RTM clauses, combined with a novel learning scheme.
result Significantly reduced computation cost with improved accuracy.
Bayesian neural networks improve uncertainty quantification in non-linear dimensionality reduction.
problem Current neural network models lack adequate uncertainty quantification.
method Deploy Markov chain Monte Carlo sampling algorithms for Bayesian inference in ANN models with latent variables.
result New research directions are needed due to fundamental challenges in neural networks with latent variables.
Proposes HSIC-Lasso for selective inference in non-linear data.
problem Detecting influential features in non-linear and high-dimensional data.
method Model-free HSIC-Lasso based on truncated Gaussians and polyhedral lemma.
result Tight control of type-I error even for small sample sizes.
Paper proposes a bias-constrained deep learning approach to non-linear estimation.
problem Designing unbiased estimators for non-linear models.
method Bias Constrained Estimator (BCE) using deep learning with bias constraints.
result Asymptotic MVUEs with Cramer Rao bound performance.
New filters for non-linear systems achieve closed-form solutions.
problem Intractability of Bayesian filtering for non-linear systems.
method Gaussian PSD Models for efficient closed-form filtering.
result Closed-form filtering with strong theoretical guarantees and adaptive error.
Develops a new model for deep structured prediction with non-linear output transformations.
problem Limited neighborhood structure and inability to transform output space in deep structured models.
method Introduces a novel model that generalizes existing approaches and maintains applicability of inference techniques.
result Demonstrates improved flexibility and applicability of deep structured models through non-linear output transformations.
New algorithm tackles non-linear utility in MNL bandits with i l d e O ( T ) ilde{O}(\sqrt{T}) i l d e O ( T ) regret.
problem Sequential assortment selection with intricate user-item interactions.
method Upper Confidence Bound principle for non-linear parametric utility functions, including neural networks.
result Achieves i l d e O ( T ) ilde{O}(\sqrt{T}) i l d e O ( T ) regret bound for neural network-based utilities. Quantum Kerr learning shows enhancements in convergence and generalization for kernel-based methods.
problem Improving convergence and generalization in kernel-based methods for quantum computing.
method Combining quantum mechanics with neural tangent kernel theory and first-order perturbation theory.
result Quantum enhancements in terms of convergence time and generalization error.
It is well-known from the work of Schönbucher (2005) that the marginal laws of a loss process can be matched by a unit increasing time inhomogeneous Markov process, whose deterministic jump intensity is called local intensity. The Stochastic Local Intensity (SLI) models such as the one proposed by Arnsdorf and Halperin…
Calibration of stochastic local volatility (SLV) models to their underlying local volatility model is often performed by numerically solving a two-dimensional non-linear forward Kolmogorov equation. We propose a novel finite volume (FV) discretization in the numerical solution of general 1D and 2D forward Kolmogorov eq…
The local linear embedding algorithm (LLE) is a non-linear dimension-reducing technique, widely used due to its computational simplicity and intuitive approach. LLE first linearly reconstructs each input point from its nearest neighbors and then preserves these neighborhood relations in the low-dimensional embedding. W…
Bayesian method estimates intervention effects in non-linear data.
problem Causal discovery from observational data with non-linear relationships.
method Gaussian Process Networks (GPN) with Bayesian estimation and Monte Carlo methods.
result Approach accurately identifies and reflects uncertainty of causal estimates.
This paper addresses graph embedding issues and introduces \strap for scalable, non-linear embeddings.
problem Preserving out-degree distributions and conflicting optimization goals on directed graphs.
method Introduces transpose proximity and \strap, a factorization-based algorithm that handles both directed and undirected graphs.
result Proposes \strap, which outperforms state-of-the-art methods in effectiveness and scalability.
Computer vision model automates residual plot assessment for diagnosing model assumptions.
problem Automating residual plot assessment for model diagnostics.
method Trains a computer vision model to predict disparity between residual distributions and reference distributions using Kullback-Leibler divergence.
result Computer vision model is less sensitive to non-linearity but more sensitive than human judgment and conventional tests.