Outlier detection in regression: conic quadratic formulations

• URL: http://arxiv.org/abs/2307.05975v1
• Date: Wed, 12 Jul 2023 07:44:13 GMT
• Title: Outlier detection in regression: conic quadratic formulations
• Authors: Andr\'es G\'omez and Jos\'e Neto
• Abstract summary: In many applications, it is important to account for the presence of outliers, i.e., corrupted input data points. Existing approaches in the literature, typically relying on the linearization of the cubic terms using big-M constraints, suffer from weak relaxation and poor performance in practice. In this work we derive stronger second-order conic relaxations that do not involve big-M constraints.
• Score: 3.04585143845864
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In many applications, when building linear regression models, it is important to account for the presence of outliers, i.e., corrupted input data points. Such problems can be formulated as mixed-integer optimization problems involving cubic terms, each given by the product of a binary variable and a quadratic term of the continuous variables. Existing approaches in the literature, typically relying on the linearization of the cubic terms using big-M constraints, suffer from weak relaxation and poor performance in practice. In this work we derive stronger second-order conic relaxations that do not involve big-M constraints. Our computational experiments indicate that the proposed formulations are several orders-of-magnitude faster than existing big-M formulations in the literature for this problem.

Related papers

• Feature selection in linear SVMs via hard cardinality constraint: a scalable SDP decomposition approach [3.7876216422538485]
  We study the embedded feature selection problem in linear Support Vector Machines (SVMs) A cardinality constraint is employed, leading to a fully explainable selection model. The problem is NP-hard due to the presence of the cardinality constraint.
  arXiv  Detail & Related papers  (2024-04-15T19:15:32Z)
• Deep Generative Symbolic Regression [83.04219479605801]
  Symbolic regression aims to discover concise closed-form mathematical equations from data. Existing methods, ranging from search to reinforcement learning, fail to scale with the number of input variables. We propose an instantiation of our framework, Deep Generative Symbolic Regression.
  arXiv  Detail & Related papers  (2023-12-30T17:05:31Z)
• Probabilistic Unrolling: Scalable, Inverse-Free Maximum Likelihood Estimation for Latent Gaussian Models [69.22568644711113]
  We introduce probabilistic unrolling, a method that combines Monte Carlo sampling with iterative linear solvers to circumvent matrix inversions. Our theoretical analyses reveal that unrolling and backpropagation through the iterations of the solver can accelerate gradient estimation for maximum likelihood estimation. In experiments on simulated and real data, we demonstrate that probabilistic unrolling learns latent Gaussian models up to an order of magnitude faster than gradient EM, with minimal losses in model performance.
  arXiv  Detail & Related papers  (2023-06-05T21:08:34Z)
• On Learning Mixture Models with Sparse Parameters [44.3425205248937]
  We study mixtures with high dimensional sparse latent parameter vectors and consider the problem of support recovery of those vectors. We provide efficient algorithms for support recovery that have a logarithmic sample complexity dependence on the dimensionality of the latent space.
  arXiv  Detail & Related papers  (2022-02-24T07:44:23Z)
• $\ell_1$-norm constrained multi-block sparse canonical correlation analysis via proximal gradient descent [0.0]
  We propose a proximal gradient descent algorithm to solve the multi-block CCA problem. We show that the resulting estimate is rate-optimal under suitable assumptions. We also describe an easy-to-implement deflation procedure to estimate multiple eigenvectors sequentially.
  arXiv  Detail & Related papers  (2022-01-14T03:35:01Z)
• A Variational Inference Approach to Inverse Problems with Gamma Hyperpriors [60.489902135153415]
  This paper introduces a variational iterative alternating scheme for hierarchical inverse problems with gamma hyperpriors. The proposed variational inference approach yields accurate reconstruction, provides meaningful uncertainty quantification, and is easy to implement.
  arXiv  Detail & Related papers  (2021-11-26T06:33:29Z)
• Solving weakly supervised regression problem using low-rank manifold regularization [77.34726150561087]
  We solve a weakly supervised regression problem. Under "weakly" we understand that for some training points the labels are known, for some unknown, and for others uncertain due to the presence of random noise or other reasons such as lack of resources. In the numerical section, we applied the suggested method to artificial and real datasets using Monte-Carlo modeling.
  arXiv  Detail & Related papers  (2021-04-13T23:21:01Z)
• Benign Overfitting of Constant-Stepsize SGD for Linear Regression [122.70478935214128]
  inductive biases are central in preventing overfitting empirically. This work considers this issue in arguably the most basic setting: constant-stepsize SGD for linear regression. We reflect on a number of notable differences between the algorithmic regularization afforded by (unregularized) SGD in comparison to ordinary least squares.
  arXiv  Detail & Related papers  (2021-03-23T17:15:53Z)
• A spectral algorithm for robust regression with subgaussian rates [0.0]
  We study a new linear up to quadratic time algorithm for linear regression in the absence of strong assumptions on the underlying distributions of samples. The goal is to design a procedure which attains the optimal sub-gaussian error bound even though the data have only finite moments.
  arXiv  Detail & Related papers  (2020-07-12T19:33:50Z)
• Conditional gradient methods for stochastically constrained convex minimization [54.53786593679331]
  We propose two novel conditional gradient-based methods for solving structured convex optimization problems. The most important feature of our framework is that only a subset of the constraints is processed at each iteration. Our algorithms rely on variance reduction and smoothing used in conjunction with conditional gradient steps, and are accompanied by rigorous convergence guarantees.
  arXiv  Detail & Related papers  (2020-07-07T21:26:35Z)
• Consistent Second-Order Conic Integer Programming for Learning Bayesian Networks [2.7473982588529653]
  We study the problem of learning the sparse DAG structure of a BN from continuous observational data. The optimal solution to this mathematical program is known to have desirable statistical properties under certain conditions. We propose a concrete early stopping criterion to terminate the branch-and-bound process in order to obtain a near-optimal solution.
  arXiv  Detail & Related papers  (2020-05-29T00:13:15Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.