Develops goodness-of-fit tests for noisy submanifold samples.
problem Testing non-linear models on noisy submanifold samples.
method Non-linear least-square problem solution and χ2 distribution application. result Residual follows χ2 distribution with parameters related to model order and dimension. New neural network models for complex functional data analysis.
problem Complex relations between functional predictors and responses.
method Function-on-Function regression models using neural networks with continuous hidden layers.
result Demonstrated power and flexibility in handling complex functional models.
This paper explores machine learning landscapes using molecular energy analogy.
problem Understanding the solution space and nature of predictions in machine learning.
method Analogy with molecular potential energy landscapes to explore machine learning landscapes.
result Emergent properties of machine learning landscapes can be related to molecular structure, thermodynamics, and kinetics.
New classifier combines locally linear kernels for fast and accurate non-linear classification.
problem Developing a fast and accurate non-linear classifier.
method Combines locally linear classifiers using a ℓ1 Multiple Kernel Learning (MKL) problem with scalable MKL training for streaming kernels. result The resulting classifier achieves high accuracy with fast inference time.
New neural network models for functional data.
problem Handling non-linear functional data.
method Functional Direct Neural Network (FDNN) and Functional Basis Neural Network (FBNN) with gradient-based optimization.
result Demonstrated effectiveness in complex functional models.
Defines simplicity of non-linear mappings using information geometry.
problem Finding a simple yet effective non-linear mapping from latent to observation space.
method Formalizes simplicity through information geometry, independent of empirical data.
result Proves basic properties of the defined simplicity measure.
New method uses reinforcement learning to sample from complex data structures efficiently.
problem Constructing reliable samples from high-dimensional polytopes for goodness-of-fit tests.
method Markov decision process and reinforcement learning for sampling.
result Demonstrated scalable tools from linear algebra for theoretical guarantees in non-linear algebra context.
Study improves understanding of network degree distributions using non-linear ERGs.
problem Lack of models capable of accounting for the variance of empirical degree distributions.
method Defined a fitness-induced variant of the two-star model to reproduce sample variance.
result Non-linear ERGs can reproduce the sample variance of empirical degree distributions.
R package for online forecasting in various fields.
problem Frequent updates of forecasts in online settings.
method Generalized setup for time-adaptive fitting of dynamical and non-linear models.
result Effective use of forecasts as model inputs in operational settings.
The log-periodic power law (LPPL) is a model of asset prices during endogenous bubbles. If the on-going development of a bubble is suspected, asset prices can be fit numerically to the LPPL law. The best solutions can then indicate whether a bubble is in progress and, if so, the bubble critical time (i.e., when the bub…
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.
Study finds sales forecasters overreact to extreme news.
problem Understanding how forecasters react to sales growth news.
method Proposes a framework with fat-tailed dynamics and linear forecasting rule.
result Forecasters overreact to significant sales growth news.
RGAM builds more accurate models by preferring linear features over non-linear ones.
problem Building accurate models when linearity assumption is poor.
method Multi-stage algorithm guided by the principle of preferring linear features.
result RGAM can fit sparse generalized additive models at scale for various data types.
Bayesian optimization speeds up parameter reconstruction in optical nano-metrology.
problem Efficiently reconstructing parameters from time-consuming measurements in optical nano-metrology.
method Combines Bayesian optimization and curve fitting for faster, more efficient model fitting.
result The presented Bayesian Target Vector Optimization scheme achieves similar reconstruction performance with fewer model function calls.
CVAE improves stock volume forecasting with advanced input variables.
problem Improving accuracy of daily stock volume forecasts.
method Conditional Variational Auto-Encoder (CVAE) with advanced input variables.
result CVAE generates non-linear forecasts with better accuracy and correlation to actual data.
New model explains market dynamics with phase transitions and non-linear interactions.
problem Understanding complex multi-asset market dynamics with phase transitions.
method Developed a Multi-Asset Non-Equilibrium Skew (MANES) model based on Langevin dynamics and McKean-Vlasov equation.
result The model accurately predicts market returns and phase transitions in both benign and distressed markets.
Optimal neuron activation functions improve neural network performance.
problem Limited expressive power of standard neuron activation functions in neural networks.
method Additive Gaussian process regression to construct individual neuron activation functions.
result Optimal neuron activation functions lead to better performance and reduced overfitting.
Improved functional data modeling with modern imputation methods.
problem Estimating complex non-linear models with sparsely and irregularly sampled functional data.
method Modified multiple imputation methods combining MissForest and Local Linear Forest.
result New imputation methods produce better estimates than existing methods.
AAnet learns non-linear archetypes from complex data.
problem Non-linear relationships in data make existing archetypal analysis methods ineffective.
method Archetypal Analysis network (AAnet) for non-linear data.
result AAnet effectively recovers and generates archetypes in non-linear domains.
Study of recurrences in earthquakes, climate, financial time-series, etc. is crucial to better forecast disasters and limit their consequences. However, almost all the previous phenomenological studies involved only a long-ranged autocorrelation function, or disregarded the multi-scaling properties induced by potential…
Tractable model explains market dynamics using Langevin and SUSY QM.
problem Understanding non-linear market dynamics and option pricing.
method Langevin dynamics mapped to QM, using SUSY to find solutions.
result NES model provides accurate option pricing with a single volatility parameter.
In this article we develop an explicit formula for pricing European options when the underlying stock price follows a non-linear stochastic differential delay equation (sdde). We believe that the proposed model is sufficiently flexible to fit real market data, and is yet simple enough to allow for a closed-form represe…
Extends neural network verification to non-linear specifications.
problem Certifying richer properties of neural networks.
method Introduces convex-relaxable specifications for verification.
result Effective verification of important properties like energy conservation and semantic consistency.
Paper presents a machine learning method to improve significance tests for misspecified linear models.
problem Misspecification of linear assumptions in social science models leads to inaccurate significance levels.
method Apply machine learning to fit ground truth function, calculate linear approximation, and adjust the estimator.
result The method significantly outperforms linear regression for non-linear ground truth functions.
We revisit the Kolmogorov-Smirnov and Cramér-von Mises goodness-of-fit (GoF) tests and propose a generalisation to identically distributed, but dependent univariate random variables. We show that the dependence leads to a reduction of the "effective" number of independent observations. The generalised GoF tests are not…
ParamBoost uses gradient boosting to create interpretable non-linear models with constraints.
problem Creating interpretable non-linear models with expert knowledge constraints.
method Gradient Boosting of cubic polynomials with specified constraints.
result ParamBoost outperforms state-of-the-art GAMs in real-world datasets.
We present a new algorithm for boosting generalized additive models for location, scale and shape (GAMLSS) that allows to incorporate stability selection, an increasingly popular way to obtain stable sets of covariates while controlling the per-family error rate (PFER). The model is fitted repeatedly to subsampled data…
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.
Researchers predict NBA player salaries using machine learning, avoiding overfitting.
problem Predicting NBA player salaries based on performance statistics.
method Selected important determinants, used Random Forest machine learning, avoided overfitting.
result Very satisfactory salary predictions identified for important factors.
SGD converges to optimal solution in perfect data fitting problem.
problem Noiseless least-squares with perfect data fitting.
method Last iterate of SGD with constant step-size.
result Convergence of SGD final iterate for non-strongly convex problem.
We show that a neural network with arbitrary depth and non-linearities, with dropout applied before every weight layer, is mathematically equivalent to an approximation to a well known Bayesian model. This interpretation might offer an explanation to some of dropout's key properties, such as its robustness to over-fitt…
SPQR package uses neural networks for flexible quantile regression.
problem Flexible modeling of non-linear relationships in quantile regression.
method Monotonic splines and neural networks for density estimation; model-agnostic covariate effects.
result Allows for non-linear and quantile-specific effects.
We provide theoretical and empirical evidence for a type of asymmetry between causes and effects that is present when these are related via linear models contaminated with additive non-Gaussian noise. Assuming that the causes and the effects have the same distribution, we show that the distribution of the residuals of …
Generative models learn manifold structure; new approach uses atlas and geodesic interpolation.
problem Challenges in representing manifolds with topology different from Euclidean space.
method Atlas Generative Models (AGMs) with hybrid latent spaces and geodesic interpolation.
result Geodesic interpolation can be extended to AGMs, improving manifold representation.
Change detection in multivariate time series has applications in many domains, including health care and network monitoring. A common approach to detect changes is to compare the divergence between the distributions of a reference window and a test window. When the number of dimensions is very large, however, the naive…
Additive regression trees are flexible non-parametric models and popular off-the-shelf tools for real-world non-linear regression. In application domains, such as bioinformatics, where there is also demand for probabilistic predictions with measures of uncertainty, the Bayesian additive regression trees (BART) model, i…
Novel pairs trading strategy for cointegrated cryptocurrencies using copulas.
problem Identifying profitable trading opportunities in cointegrated cryptocurrency pairs.
method Linear and non-linear cointegration tests, correlation coefficient, copula families, back-testing.
result The strategy outperforms buy-and-hold trading strategies in profitability and risk-adjusted returns.
The distribution of the return intervals τ between volatilities above a threshold q for financial records has been approximated by a scaling behavior. To explore how accurate is the scaling and therefore understand the underlined non-linear mechanism, we investigate intraday datasets of 500 stocks which consist of …
Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the curse of dimensionality when the number of summary statistics is increased. Here w…
Improved interpretability methods for ML models using local regressions and variable importance.
problem Inability of existing interpretability methods to provide reliable explanations for ML models, especially in high-dimensional problems with irrelevant features and non-linear relationships.
method Introduces VarImp and SupClus methods using local regressions with weighted distance considering variable importance.
result VarImp and SupClus methods yield better explanations than state-of-the-art approaches, especially in high-dimensional problems with irrelevant features and non-linear relationships.
A ML model accurately replicates chaotic dynamics across various parameters.
problem Replicating chaotic characteristics of non-linear dynamics using machine learning.
method A ML model trained to predict one-step-ahead states from historic states captures bifurcation diagrams and Lyapunov exponents universally.
result Variational quantum circuit outperforms classical models in reproducing long-term chaotic characteristics.
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. …
CNR uses convex optimization to estimate conditional distributions.
problem Estimating uncertainty in predictions and posterior conditional distributions.
method Convex optimization of a posterior defined via non-linear transformations on Gaussians.
result CNR can fit arbitrary conditional distributions, including multimodal and non-symmetric ones.
New models outperform deep ones in survival analysis without complex parameters.
problem Improving survival analysis models without overly complex parameters.
method Semi-parametric models inspired from mixtures of experts.
result Interpretable semi-parametric models perform equally well or better than deep models.
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.
Method estimates dynamic treatment effects using machine learning and g-estimation.
problem Estimating treatment effects over time with multiple treatments and potential future outcomes.
method Double/debiased machine learning framework for dynamic treatment effects, extending Neyman orthogonal cross-fitted g-estimation. result Provides finite sample guarantees and allows for non-linear effect heterogeneity and high-dimensional parameterizations.
In many scientific disciplines structures in high-dimensional data have to be found, e.g., in stellar spectra, in genome data, or in face recognition tasks. In this work we present a novel approach to non-linear dimensionality reduction. It is based on fitting K-nearest neighbor regression to the unsupervised regressio…
FSNN learns causal relationships in complex systems using neural nets.
problem Inferring causality in directed cyclic graphs.
method Constructs a non-linear system of ODEs using feed forward neural nets.
result Accurately models complex, non-linear systems with causal relationships.