PROMPT: Parallel Iterative Algorithm for $\ell_{p}$ norm linear regression via Majorization Minimization with an application to semi-supervised graph learning

• URL: http://arxiv.org/abs/2110.12190v1
• Date: Sat, 23 Oct 2021 10:19:11 GMT
• Title: PROMPT: Parallel Iterative Algorithm for $\ell_{p}$ norm linear regression via Majorization Minimization with an application to semi-supervised graph learning
• Authors: R.Jyothi and P.Babu
• Abstract summary: We consider the problem of $ell_p$ norm linear regression, which has several applications such as in sparse recovery, data clustering, and semi-supervised learning. We propose an iterative algorithm : Parallel IteRative AlgOrithM for $ell_P$ norm regression via MajorizaTion Minimization (PROMPT)
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper, we consider the problem of $\ell_{p}$ norm linear regression, which has several applications such as in sparse recovery, data clustering, and semi-supervised learning. The problem, even though convex, does not enjoy a closed-form solution. The state-of-the-art algorithms are iterative but suffer from convergence issues, i.e., they either diverge for p>3 or the convergence to the optimal solution is sensitive to the initialization of the algorithm. Also, these algorithms are not generalizable to every possible value of $p$. In this paper, we propose an iterative algorithm : Parallel IteRative AlgOrithM for $\ell_{P}$ norm regression via MajorizaTion Minimization (PROMPT) based on the principle of Majorization Minimization and prove that the proposed algorithm is monotonic and converges to the optimal solution of the problem for any value of $p$. The proposed algorithm can also parallelly update each element of the regression variable, which helps to handle large scale data efficiently, a common scenario in this era of data explosion. Subsequently, we show that the proposed algorithm can also be applied for the graph based semi-supervised learning problem. We show through numerical simulations that the proposed algorithm converges to the optimal solution for any random initialization and also performs better than the state-of-the-art algorithms in terms of speed of convergence. We also evaluate the performance of the proposed algorithm using simulated and real data for the graph based semi-supervised learning problem.

Related papers

• Improved Parallel Algorithm for Non-Monotone Submodular Maximization under Knapsack Constraint [0.0]
  This work proposes an efficient parallel algorithm for non-monomodular size under a knapsack constraint. Our algorithm improves the existing parallel one from $8+epsilon$ to $7+epsilon$ with $O(log n)$ adaptive complexity.
  arXiv  Detail & Related papers  (2024-09-06T17:17:52Z)
• A Cubic-regularized Policy Newton Algorithm for Reinforcement Learning [9.628032156001073]
  We propose two policy Newton algorithms that incorporate cubic regularization. Both algorithms employ the likelihood ratio method to form estimates of the gradient and Hessian of the value function. In particular, the sample complexity of our algorithms to find an $epsilon$-SOSP is $O(epsilon-3.5)$, which is an improvement over the state-of-the-art sample complexity of $O(epsilon-4.5)$.
  arXiv  Detail & Related papers  (2023-04-21T13:43:06Z)
• Kernel Packet: An Exact and Scalable Algorithm for Gaussian Process Regression with Mat\'ern Correlations [23.560067934682294]
  We develop an exact and scalable algorithm for one-dimensional Gaussian process regression with Mat'ern correlations. The proposed algorithm is significantly superior to the existing alternatives in both the computational time and predictive accuracy.
  arXiv  Detail & Related papers  (2022-03-07T03:30:35Z)
• Provably Faster Algorithms for Bilevel Optimization [54.83583213812667]
  Bilevel optimization has been widely applied in many important machine learning applications. We propose two new algorithms for bilevel optimization. We show that both algorithms achieve the complexity of $mathcalO(epsilon-1.5)$, which outperforms all existing algorithms by the order of magnitude.
  arXiv  Detail & Related papers  (2021-06-08T21:05:30Z)
• Linear regression with partially mismatched data: local search with theoretical guarantees [9.398989897176953]
  We study an important variant of linear regression in which the predictor-response pairs are partially mismatched. We use an optimization formulation to simultaneously learn the underlying regression coefficients and the permutation corresponding to the mismatches. We prove that our local search algorithm converges to a nearly-optimal solution at a linear rate.
  arXiv  Detail & Related papers  (2021-06-03T23:32:12Z)
• Online Model Selection for Reinforcement Learning with Function Approximation [50.008542459050155]
  We present a meta-algorithm that adapts to the optimal complexity with $tildeO(L5/6 T2/3)$ regret. We also show that the meta-algorithm automatically admits significantly improved instance-dependent regret bounds.
  arXiv  Detail & Related papers  (2020-11-19T10:00:54Z)
• Single-Timescale Stochastic Nonconvex-Concave Optimization for Smooth Nonlinear TD Learning [145.54544979467872]
  We propose two single-timescale single-loop algorithms that require only one data point each step. Our results are expressed in a form of simultaneous primal and dual side convergence.
  arXiv  Detail & Related papers  (2020-08-23T20:36:49Z)
• A Two-Timescale Framework for Bilevel Optimization: Complexity Analysis and Application to Actor-Critic [142.1492359556374]
  Bilevel optimization is a class of problems which exhibit a two-level structure. We propose a two-timescale approximation (TTSA) algorithm for tackling such a bilevel problem. We show that a two-timescale natural actor-critic policy optimization algorithm can be viewed as a special case of our TTSA framework.
  arXiv  Detail & Related papers  (2020-07-10T05:20:02Z)
• Provably Convergent Working Set Algorithm for Non-Convex Regularized Regression [0.0]
  This paper proposes a working set algorithm for non-regular regularizers with convergence guarantees. Our results demonstrate high gain compared to the full problem solver for both block-coordinates or a gradient solver.
  arXiv  Detail & Related papers  (2020-06-24T07:40:31Z)
• Private Stochastic Convex Optimization: Optimal Rates in Linear Time [74.47681868973598]
  We study the problem of minimizing the population loss given i.i.d. samples from a distribution over convex loss functions. A recent work of Bassily et al. has established the optimal bound on the excess population loss achievable given $n$ samples. We describe two new techniques for deriving convex optimization algorithms both achieving the optimal bound on excess loss and using $O(minn, n2/d)$ gradient computations.
  arXiv  Detail & Related papers  (2020-05-10T19:52:03Z)
• Second-order Conditional Gradient Sliding [79.66739383117232]
  We present the emphSecond-Order Conditional Gradient Sliding (SOCGS) algorithm. The SOCGS algorithm converges quadratically in primal gap after a finite number of linearly convergent iterations. It is useful when the feasible region can only be accessed efficiently through a linear optimization oracle.
  arXiv  Detail & Related papers  (2020-02-20T17:52:18Z)

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.