In this paper, we address the challenging problem of selecting tuning parameters for high-dimensional sparse regression. We propose a simple and computationally efficient method, called path thresholding (PaTh), that transforms any tuning parameter-dependent sparse regression algorithm into an asymptotically tuning-fre…
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48 results for “path regression”
Proposes an efficient shrinkage path for ridge regression.
problem Ill-conditioned data in linear models.
method A new generalized ridge regression shrinkage path that minimizes MSE risk.
result The path is as short as possible while maintaining optimal trade-off.
Estimates path-valued data using signature metrics and local kernels.
problem Nonparametric regression and classification for path-valued data.
method Combines signature transform and local kernel regression.
result Establishes convergence bounds and demonstrates competitive accuracy.
Paper develops approximation and statistical theory for signature-based path regression.
problem Understanding how fast signatures approximate continuous path functionals.
method Develops \(L^2\) approximation rate for smooth functionals of Itô diffusions and establishes consistency of statistical learning procedures.
result Signature-based methods improve prediction over handcrafted features in various real-data applications.
PSLR classifies functional data with scalar covariates using path signatures.
problem Classical functional logistic regression models have limitations in capturing nonlinear and cross-channel dependencies.
method PSLR uses truncated path signatures to create a basis-free representation of functional data.
result PSLR outperforms traditional functional classifiers in accuracy and robustness, especially under non-uniform sampling.
We study pathwise invariances of centred random fields that can be controlled through the covariance. A result involving composition operators is obtained in second-order settings, and we show that various path properties including additivity boil down to invariances of the covariance kernel. These results are extended…
Researchers compare different gradient methods for ridge regression, finding conjugate gradients have similar performance.
problem Comparing statistical properties of different gradient methods in ridge regression.
method Explicit non-standard error decomposition to bound prediction error of conjugate gradient iterates.
result Conjugate gradient iterates share optimality properties with gradient flow and ridge regression up to a constant factor.
Nested model averaging improves high-dimensional linear regression performance.
problem High-dimensional linear regression with predictor ordering impact.
method Combining model averaging with regularized estimators on the solution path.
result Nested model averaging with lasso and SLOPE outperforms competing methods.
Efficient algorithms for clustered Lasso and OSCAR reduce computational costs.
problem High dimensional regression with feature clustering.
method Efficient path algorithms for clustered Lasso and OSCAR, reducing computational costs.
result Proposed algorithms are more efficient than existing methods in numerical experiments.
PAN uses path integrals for graph convolution and pooling, improving GNN performance.
problem Designing efficient graph convolution and pooling for graph neural networks.
method Path integral based graph convolution and pooling using learnable weights for path lengths.
result PAN achieves state-of-the-art performance on various graph classification/regression tasks.
Paper tackles DR problem with scalable signature-based approach.
problem Memory and computation cost issues in DR solutions.
method Signature-based features, novel distance approximator.
result Proposes scalable DR solution with reduced estimation uncertainty.
New method identifies causal relationships in presence of hidden variables.
problem Identifying causal relationships when hidden variables exist.
method Established sufficient conditions and introduced a search algorithm.
result Proved soundness and completeness of the search algorithm.
Paper proposes method for generating paths of stochastic volatility CGMY process for option pricing.
problem Generating accurate sample paths for stochastic volatility models for option pricing.
method Monte-Carlo method for European and American options, least square regression for calibration.
result Calibrated model parameters to S\&P 100 index options market using path-dependent options.
We consider the generic regularized optimization problem . Efron, Hastie, Johnstone and Tibshirani [Ann. Statist. 32 (2004) 407--499] have shown that for the LASSO--that is, if is squared error loss and is the norm of --the opti…
We study the complexity of the entire regularization path for least squares regression with 1-norm penalty, known as the Lasso. Every regression parameter in the Lasso changes linearly as a function of the regularization value. The number of changes is regarded as the Lasso's complexity. Experimental results using exac…
Selecting important features in non-linear or kernel spaces is a difficult challenge in both classification and regression problems. When many of the features are irrelevant, kernel methods such as the support vector machine and kernel ridge regression can sometimes perform poorly. We propose weighting the features wit…
Modern navigation services often provide multiple paths connecting the same source and destination for users to select. Hence, ranking such paths becomes increasingly important, which directly affects the service quality. We present PathRank, a data-driven framework for ranking paths based on historical trajectories us…
The paper proposes a method to improve random forest classification accuracy by weighting trees based on their decision path reliability.
problem Random forests' uniform voting fails to correct errors in regions where incorrect tree representations outnumber correct ones.
method The paper introduces using the structural pattern of each tree's decision path as an instance-adaptive reliability signal to identify and weight more reliable trees.
result Using the proposed method yields a statistically significant accuracy improvement over RF on 36 binary classification benchmarks.
Deep learning predicts path-dependent processes from historical data.
problem Predicting path-dependent processes using historical data.
method Nonparametric regression with deep neural networks.
result Deep learning method converges to theoretical predictions as observation frequency increases.
The paper develops a new simulation technique for estimating conditional expectations in financial models.
problem Estimating conditional expectations in financial models with expensive simulation of endogenous variables.
method Introduces a hierarchical simulation scheme with oversimplified defaults to address variance issues.
result The hierarchical simulation technique significantly improves the success of neural net regression for conditional expectation estimation.
Although various linear log-distance path loss models have been developed, advanced models are requiring to more accurately and flexibly represent the path loss for complex environments such as the urban area. This letter proposes an artificial neural network (ANN) based multi-dimensional regression framework for path …
We propose a sparse and low-rank tensor regression model to relate a univariate outcome to a feature tensor, in which each unit-rank tensor from the CP decomposition of the coefficient tensor is assumed to be sparse. This structure is both parsimonious and highly interpretable, as it implies that the outcome is related…
Minimum energy paths for transitions such as atomic and/or spin rearrangements in thermalized systems are the transition paths of largest statistical weight. Such paths are frequently calculated using the nudged elastic band method, where an initial path is iteratively shifted to the nearest minimum energy path. The co…
The paper compares machine learning methods with traditional techniques for pricing and sensitivities of financial products with path-dependent structures.
problem Evaluating financial products with early-termination clauses, especially those with path-dependent structures.
method The paper compares regression methods including randomized recurrent and feed-forward neural networks, and a novel approach using signatures of the underlying price process, with traditional polynomial basis functions for pricing and sensitivities.
result Machine learning algorithms often match the accuracy and efficiency of traditional methods for Asian and look-back options, while randomized neural networks are best for callable certificates.
Sparse model selection is ubiquitous from linear regression to graphical models where regularization paths, as a family of estimators upon the regularization parameter varying, are computed when the regularization parameter is unknown or decided data-adaptively. Traditional computational methods rely on solving a set o…
Compositional data have two unique characteristics compared to typical multivariate data: the observed values are nonnegative and their summand is exactly one. To reflect these characteristics, a specific regularized regression model with linear constraints is commonly used. However, linear constraints incur additional…
Unified representation for tree ensembles indexed by nodes
problem Unifying geometric object for tree ensembles indexed by nodes
method KPP indexes feature map by nodes, weighted by path metric
result Unified non-diagonal Gram for prediction, additive attribution, robust radius, and risk bounds
This paper introduces a method to approximate Gaussian process regression by representing the problem as a stochastic differential equation and using variational inference to approximate solutions. The approximations are compared with full GP regression and generated paths are demonstrated to be indistinguishable from …
The calculation of minimum energy paths for transitions such as atomic and/or spin re-arrangements is an important task in many contexts and can often be used to determine the mechanism and rate of transitions. An important challenge is to reduce the computational effort in such calculations, especially when ab initio …
Learning from the past, predicting the statistics for the future, learning an evolving systemq-fin.ST
We bring the theory of rough paths to the study of non-parametric statistics on streamed data. We discuss the problem of regression where the input variable is a stream of information, and the dependent response is also (potentially) a stream. A certain graded feature set of a stream, known in the rough path literature…
Transformer adapts to graphs with adaptive attention and auto-regressive decoding.
problem Transformers struggle with graph data due to non-sequential nature.
method Proposes GRAT, a Transformer variant with adaptive attention and auto-regressive decoding.
result GRAT achieves state-of-the-art performance on molecule property predictions and generation tasks.
Flow Matching enables robust training of CNFs with various probability paths.
problem Training Continuous Normalizing Flows (CNFs) at large scales.
method Flow Matching (FM) is a simulation-free approach for training CNFs by regressing vector fields of conditional probability paths.
result Flow Matching with diffusion paths yields more robust and stable training compared to diffusion-based methods.
PathBoost boosts graph-level predictions using path-based features.
problem Graph-level classification and regression challenges.
method Gradient tree boosting method for graph-level prediction.
result PathBoost outperforms graph neural networks and graph kernel approaches in many cases.
New simulation approaches to evaluating path-dependent options without matrix inversion issues nor Euler bias are evaluated. They employ three main contributions: Stochastic approximation replaces regression in the LSM algorithm; Explicit weak solutions to stochastic differential equations are developed and applied to …
New method generates realistic financial price paths with drawdowns.
problem Lack of realistic drawdown scenarios in financial simulations.
method Variational autoencoder with drawdown reconstruction loss and path signatures.
result Simulated paths closely match empirical drawdown data.
Bias - variance decomposition of the expected error defined for regression and classification problems is an important tool to study and compare different algorithms, to find the best areas for their application. Here the decomposition is introduced for the survival analysis problem. In our experiments, we study bias -…
Solar: solution path averaging for fast and accurate variable selection in high-dimensional datastat.ML
Solar algorithm selects variables faster and more accurately in high-dimensional data.
problem Variable selection in high-dimensional data with high accuracy and stability.
method Subsample-ordered least-angle regression (solar) and its coordinate descent generalization (solar-cd) using norm solution path averaging.
result Solar selects variables with high accuracy and stability, reducing redundant variable selection.
Paper develops SKPD framework for signal region detection in image regression.
problem Limited research on image region detection in high-resolution image regression.
method Sparse Kronecker Product Decomposition (SKPD) framework for matrices and tensors.
result Computed solutions converge to truth with guaranteed consistency.
Optimal computational and statistical rates of convergence for sparse nonconvex learning problemsstat.ML
We provide theoretical analysis of the statistical and computational properties of penalized -estimators that can be formulated as the solution to a possibly nonconvex optimization problem. Many important estimators fall in this category, including least squares regression with nonconvex regularization, generalized …
New algorithmic view of ℓ2 regularization using ODEs and path-following methods.
problem Optimizing convex loss functions with ℓ2 regularization.
method Established an equivalence between ℓ2-regularized solution paths and ODEs, proposing path-following algorithms based on homotopy methods and numerical ODE solvers.
result The solution path can be viewed as a hybrid of gradient descent and Newton method, providing novel schemes to choose grid points and reducing computational cost.
We propose a representation of Gaussian processes (GPs) based on powers of the integral operator defined by a kernel function, we call these stochastic processes integral Gaussian processes (IGPs). Sample paths from IGPs are functions contained within the reproducing kernel Hilbert space (RKHS) defined by the kernel fu…
PathNNs improve graph neural networks by distinguishing non-isomorphic graphs.
problem Limitations of standard GNNs in distinguishing non-isomorphic graphs.
method Proposes PathNNs that aggregate paths to update node representations.
result Two variants of PathNNs are strictly more powerful than 1-WL algorithm.
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.
We propose a semismooth Newton algorithm for pathwise optimization (SNAP) for the LASSO and Enet in sparse, high-dimensional linear regression. SNAP is derived from a suitable formulation of the KKT conditions based on Newton derivatives. It solves the semismooth KKT equations efficiently by actively and continuously s…
Parallel American Monte Carloq-fin.CP
In this paper we introduce a new algorithm for American Monte Carlo that can be used either for American-style options, callable structured products or for computing counterparty credit risk (e.g. CVA or PFE computation). Leveraging least squares regressions, the main novel feature of our algorithm is that it can be fu…
Many model selection algorithms produce a path of fits specifying a sequence of increasingly complex models. Given such a sequence and the data used to produce them, we consider the problem of choosing the least complex model that is not falsified by the data. Extending the selected-model tests of Fithian et al. (2014)…
This paper presents the asymptotic behavior of a linear instrumental variables (IV) estimator that uses a ridge regression penalty. The regularization tuning parameter is selected empirically by splitting the observed data into training and test samples. Conditional on the tuning parameter, the training sample creates …
Feature selection is a standard approach to understanding and modeling high-dimensional classification data, but the corresponding statistical methods hinge on tuning parameters that are difficult to calibrate. In particular, existing calibration schemes in the logistic regression framework lack any finite sample guara…