BALSON optimizes parameters with Bayesian approach and Dirichlet distribution.
problem Data fitting with nonnegative L1-norm constraints.
method Bayesian approach, Gaussian likelihood, Dirichlet distribution, sampling methods.
result BALSON outperforms conventional methods in polynomial fitting.
Study tightens bounds for interpolating noisy data using minimum l1-norm.
problem Predicting noisy data with minimum l1-norm interpolation.
method Provided matching upper and lower bounds for prediction error.
result Tight consistency up to negligible terms for d≫n. A new algorithm optimizes L1-norm error fitting problems efficiently.
problem Optimizing L1-norm error fitting models with data aggregation.
method Data aggregation-based algorithm with monotonic convergence to global optimum.
result The proposed algorithm optimally solves any L1-norm error fitting model.
Study models arrival rates and cancellation rates of limit orders in Borsa Istanbul.
problem Understanding order dynamics in Borsa Istanbul's stock market.
method Used limit order book data from Garanti Bank. Tested three discrete probability distributions and two theoretical models for arrival rates. Examined cancellation rates using L1 norms.
result Modelled daily, weekly, and monthly arrival rates of limit orders in the first fifteen bid and ask price levels.
Proposes a new method for hyperspectral image dimensionality reduction.
problem Highly correlated noisy hyperspectral images.
method Trace Lasso-L1 Graph Cut method using L1-norm for robustness and sparsity.
result Optimal projection matrix maximizing between-class dispersion to within-class dispersion.
A fast algorithm for L1-norm kernel PCA with convergence analysis.
problem Finding an optimal solution for L1-norm kernel PCA due to its non-convexity and non-smoothness.
method A fixed-point type algorithm that iteratively computes binary weights for each observation, based on a geometrically interpretable reformulation of the problem.
result The algorithm converges to a local optimal solution in a finite number of steps and the sequence of objective values converges at a linear rate.
New algorithm solves GDS with faster convergence and FDR control.
problem Generalized Dantzig Selector estimation problem.
method Primal-dual proximal extragradient algorithm with saddle-point reformulation.
result Achieves optimal O(1/k) convergence rate. Novel L1-norm and L2-norm LDA methods improve discriminant analysis.
problem Improving linear discriminant analysis for robustness and adaptability.
method Proposes L1BLDA and L2BLDA using Bhattacharyya error bound, maximizing between-class scatters and minimizing within-class scatters.
result Proposed methods avoid SSS and have no rank limit, demonstrating robust performance and effectiveness.
We study the deformation of the three-dimensional conformal structures by the Ricci flow. We drive the evolution equation of Cotton-York tensor and the L1-norm of it under the Ricci flow. In particular, we investigate the behavior of the L1-norm of the Cotton-York tensor under the Ricci flow on three-dimensional simply…
New method solves rank-1 L1-norm TUCKER2 decomposition efficiently.
problem Exact solution to rank-1 L1-norm TUCKER2 decomposition of tensors.
method Proved equivalent to combinatorial optimization, derived two algorithms.
result L1-TUCKER2 outperforms other methods in tensor approximation for outlier-corrupted data.
New algorithms improve L1 PCA performance.
problem Optimizing PCA with L1 norm for better data reduction.
method Iteratively reweighted least squares algorithms.
result Proposed algorithms outperform existing methods.
A l1-norm penalized orthogonal forward regression (l1-POFR) algorithm is proposed based on the concept of leaveone- out mean square error (LOOMSE). Firstly, a new l1-norm penalized cost function is defined in the constructed orthogonal space, and each orthogonal basis is associated with an individually tunable regulari…
Proposes an optimization framework for sparse robust subspace estimation.
problem Sparse robust one-dimensional subspace estimation.
method l1-norm regularization, linear relaxation, simple ratios, sorting techniques.
result Achieves global optimality for sparse robust subspace with polynomial time efficiency.
A new algorithm calculates L1-norm principal components efficiently for large datasets.
problem Efficiently calculating L1-norm principal components for large datasets.
method Suboptimal algorithm with cost comparable to standard PCA, using bit flipping.
result Achieves higher L1-PC optimization metric than alternatives.
Study investigates estimation error in EMHMM simulations.
problem Estimation error in Hidden Markov Models (HMMs) with EMHMM.
method Simulation study using variational Bayesian inference.
result KL divergence and L1-norm relate to estimation error and ground-truth HMM parameters.
A typical approach in estimating the learning rate of a regularized learning scheme is to bound the approximation error by the sum of the sampling error, the hypothesis error and the regularization error. Using a reproducing kernel space that satisfies the linear representer theorem brings the advantage of discarding t…
Targeting at sparse learning, we construct Banach spaces B of functions on an input space X with the properties that (1) B possesses an l1 norm in the sense that it is isometrically isomorphic to the Banach space of integrable functions on X with respect to the counting measure; (2) point evaluations are continuous lin…
To recover a sparse signal from an underdetermined system, we often solve a constrained L1-norm minimization problem. In many cases, the signal sparsity and the recovery performance can be further improved by replacing the L1 norm with a "weighted" L1 norm. Without any prior information about nonzero elements of the si…
This study evaluates Lx-norm penalties for resolving complex LC-MS data.
problem Resolving complex LC-MS data with rotational ambiguity.
method Simulated LC-MS data and grid search strategy to compare L0-, L1-, and L2-norm penalties.
result L1-norm penalty (Lasso) provides more sparse solutions and reduces rotational ambiguity.
Two sparsity-aware NSAF algorithms improve sparse system identification with lower complexity.
problem Sparse system identification with improved performance and lower complexity.
method Gradient descent method to minimize combined cost function and l1-norm penalty on filter coefficients.
result Proposed algorithms achieve comparable performance with lower computational complexity.
Vertex distortion measures how far lattice knots deviate from straight lines.
problem Measuring how much lattice knots deviate from straight paths.
method Analogous to smooth knots, study vertex distortion in lattice knots.
result Vertex distortion is 1 only for the unknot and can be arbitrarily high.
Robust tensor ring completion improves tensor recovery accuracy and efficiency.
problem Tensor completion sensitivity to sparse components.
method Robust Tensor Ring Completion (RTRC) with weighted nuclear norms and l1 regularization.
result Exact recovery guarantees and superior performance in various tasks.
Network anomaly detection is still a vibrant research area. As the fast growth of network bandwidth and the tremendous traffic on the network, there arises an extremely challengeable question: How to efficiently and accurately detect the anomaly on multiple traffic? In multi-task learning, the traffic consisting of flo…
QAPCA uses quantum annealing for robust PCA.
problem Outliers in data skew L2-norm principal components.
method Quantum annealing for L1-norm optimization.
result QAPCA's reconstruction error is comparable to L1-BF.
Proposes a new SVM model for binary classification with theoretical and practical advantages.
problem Binary classification in supervised learning.
method Quadratic surface support vector machine with L1 norm regularization.
result The model can detect true sparsity patterns and is efficient for both synthetic and real data.
Develops efficient method for nonconvex problems using Regula Falsi.
problem Nonconvex inverse problems with likelihood constraints.
method Regula Falsi root-finding techniques applied to level-set formulations.
result Proves extension of level-set methods to nonconvex problems.
Noise injection before gradient steps helps in regularization for neural networks.
problem Improving generalization in overparametrized neural networks.
method Injecting small noise perturbations before computing gradient steps, especially in layer-wise fashion.
result Small noise perturbations can explicitly regularize neural networks without variance explosion.
Uniform convergence of interpolators proven for Gaussian data.
problem Interpolation learning in high-dimensional linear regression with Gaussian data.
method Generic uniform convergence guarantee in terms of Gaussian width.
result Consistency of interpolators for minimum-norm and near-minimal-norm cases.
This paper addresses the problem of sparsity penalized least squares for applications in sparse signal processing, e.g. sparse deconvolution. This paper aims to induce sparsity more strongly than L1 norm regularization, while avoiding non-convex optimization. For this purpose, this paper describes the design and use of…
Paper compares optimization methods for sparse NCP decomposition of tensors.
problem Efficiently extract meaningful nonnegative and sparse components from tensors.
method Sparse NCP decomposition with l1-norm regularization and block coordinate descent.
result Comparison of optimization methods for tensor decomposition effectiveness and speed.
For supervised and unsupervised learning, positive definite kernels allow to use large and potentially infinite dimensional feature spaces with a computational cost that only depends on the number of observations. This is usually done through the penalization of predictor functions by Euclidean or Hilbertian norms. In …
New variational model preserves image contrasts and features using Weingarten map minimization.
problem Image reconstruction with preservation of contrasts and features.
method Variational model with L1 norm of Weingarten map, ADMM algorithm, gradient descent. result The proposed models preserve image contrasts and features efficiently.
New theoretical framework improves error rates for sparse learning with convex regularization.
problem Improving error rates for sparse learning with convex regularization.
method Proposed a new theoretical framework using common assumptions to derive high-dimensional estimation bounds.
result Improved error rates for L1, Slope, and Group L1-L2 regularizations, matching or exceeding existing results.
Most of the existing methods for sparse signal recovery assume a static system: the unknown signal is a finite-length vector for which a fixed set of linear measurements and a sparse representation basis are available and an L1-norm minimization program is solved for the reconstruction. However, the same representation…
Smoothed analysis shows that many classes become learnable from positive-only samples.
problem Learning from positive-only samples is challenging due to negative results in worst-case settings.
method Smoothed analysis of positive-only learning, assuming samples from a reference distribution smooth with respect to the true distribution.
result All VC classes become learnable in the smoothed model with O(VC/ε2) positive samples for ε classification error. Proposes a method to estimate sparse low-rank matrices from noisy data.
problem Estimating sparse low-rank matrices from noisy observations.
method Objective function with non-convex penalties, ADMM algorithm.
result Proposed method outperforms convex methods in estimating sparse low-rank matrices.
Paper proposes a new robust LDA method using L1,2-norm ratio minimization.
problem Outliers sensitivity in traditional LDA methods.
method L1,2-norm ratio minimization, novel efficient algorithm.
result The proposed method is effective and converges fast.
New algorithms solve robust MDPs efficiently, significantly faster than existing methods.
problem Computing robust MDP solutions with uncertainty in transition probabilities is computationally expensive.
method Partial policy iteration and fast robust Bellman operator computation methods.
result The proposed methods are many orders of magnitude faster than state-of-the-art approaches.
New L0 norm added to TDA for market analysis.
problem Improving TDA tools for market prediction.
method Defined and applied L0 norm in TDA for four markets.
result Enhanced TDA tools for market analysis.
Characterizes functions representable by infinite-width ReLU networks with bounded weights.
problem Understanding function representation in overparameterized neural networks.
method Analyzes functions in Ws,1(R) spaces and their Radon transform. result All functions in Ws,1(R) can be represented with bounded norm. Adaptive filtering algorithms operating in reproducing kernel Hilbert spaces have demonstrated superiority over their linear counterpart for nonlinear system identification. Unfortunately, an undesirable characteristic of these methods is that the order of the filters grows linearly with the number of input data. This …
The problem of biclustering consists of the simultaneous clustering of rows and columns of a matrix such that each of the submatrices induced by a pair of row and column clusters is as uniform as possible. In this paper we approximate the optimal biclustering by applying one-way clustering algorithms independently on t…
New method improves brain activity analysis with better amplitude and source selection.
problem Improving brain activity analysis with high temporal and spatial resolution.
method Iterative reweighted Mixed-Norm Estimate (irMxNE) for solving non-convex optimization problems.
result Improves on standard Mixed Norm Estimate (MxNE) in amplitude bias, support recovery, and stability.
Minimal SVM reduces support vectors for better classification.
problem Finding optimal hyperplane for classification with fewer support vectors.
method Proposes a Minimal SVM using L0.5 norm on slack variables.
result Increases classification performance by reducing support vectors.
Approximate dynamic programming is a popular method for solving large Markov decision processes. This paper describes a new class of approximate dynamic programming (ADP) methods- distributionally robust ADP-that address the curse of dimensionality by minimizing a pessimistic bound on the policy loss. This approach tur…
It is well known that quantile regression model minimizes the portfolio extreme risk, whenever the attention is placed on the estimation of the response variable left quantiles. We show that, by considering the entire conditional distribution of the dependent variable, it is possible to optimize different risk and perf…
SPCA improves PCA by learning from simple to complex samples.
problem Noise and outliers in complex data.
method Self-paced Principal Component Analysis (SPCA) that integrates samples from simple to more complex.
result SPCA improves state-of-the-art results on popular datasets.
New method controls false discovery rate in learning Gaussian MRF structures.
problem Learning the structure of Gaussian MRFs from data, especially when p >> n, leads to false edges.
method Proposes nsSLOPE using sorted l1-norm regularization to control false discovery rate.
result Controls false discovery rate in learning the structure of Gaussian MRFs.