This paper deals with sparse feature selection and grouping for classification and regression. The classification or regression problems under consideration consists in minimizing a convex empirical risk function subject to an constraint, a pairwise constraint, or a pairwise constraint. …
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48 results for “Outer-approximation algorithms”
New framework solves low-rank optimization problems to certifiable optimality.
problem Low-rank optimization problems with certifiable solutions.
method Mixed-Projection Conic Optimization framework using symmetric projection matrices and outer-approximation algorithms.
result Solves low-rank problems to certifiable optimality, outperforming existing methods.
Considering mean-variance portfolio problems with uncertain model parameters, we contrast the classical absolute robust optimization approach with the relative robust approach based on a maximum regret function. Although the latter problems are NP-hard in general, we show that tractable inner and outer approximations e…
Neural network approximates weakly efficient frontier of convex vector optimization problems.
problem Approximating the weakly efficient frontier of convex vector optimization problems.
method Designing a neural network architecture to approximate the weakly efficient frontier of convex vector optimization problems (CVOP) satisfying Slater's condition.
result The proposed algorithm effectively approximates the true weakly efficient frontier of CVOPs, even for large problems.
We study a cutting-plane method for semidefinite optimization problems (SDOs), and supply a proof of the method's convergence, under a boundedness assumption. By relating the method's rate of convergence to an initial outer approximation's diameter, we argue that the method performs well when initialized with a second-…
Method approximates Lipschitz domains with smoother shapes.
problem Approximating bounded Lipschitz domains.
method Sequence of smooth, bounded domains with weak curvatures.
result Uniform isocapacitary estimates for approximating sets.
We propose a data-driven approach to quantify the uncertainty of models constructed by kernel methods. Our approach minimizes the needed distributional assumptions, hence, instead of working with, for example, Gaussian processes or exponential families, it only requires knowledge about some mild regularity of the measu…
The paper improves confidence ellipsoids for ridge regression with PAC bounds.
problem Uncertainty quantification in ridge regression for insufficiently exciting inputs.
method Extension of SPS EOA algorithm to ridge regression with PAC bounds.
result Explicitly shows how regularization parameter affects region sizes and provides tighter bounds.
A new method, Residual-Permuted Sums, improves confidence region construction for linear regression models.
problem Constructing reliable confidence regions for linear regression models with non-symmetric noise.
method Residual-Permuted Sums (RPS) method, which permutes residuals instead of perturbing their signs.
result RPS provides exact finite sample coverage probabilities and is uniformly strongly consistent.
The paper develops a method to create non-asymptotic confidence ellipsoids for linear regression without strong noise distribution assumptions.
problem Constructing reliable confidence regions for linear regression with finite sample sizes and general noise distributions.
method The paper introduces the SPS EOA algorithm to create non-asymptotically guaranteed confidence ellipsoids for linear regression problems.
result The sizes of SPS outer ellipsoids are shown to decrease at the optimal rate for linear regression problems.
This paper analyzes the sample complexity of SPS method for scalar linear regression.
problem Analyzing the sample complexity of the Sign-Perturbed Sums (SPS) identification method.
method The paper provides high probability upper bounds for the sizes of SPS confidence intervals under different sets of assumptions.
result The sizes of SPS confidence intervals shrink at a geometric rate around the true parameter, if observation noises are subgaussian.
A model-based optimal experiment design (OED) of nonlinear systems is studied. OED represents a methodology for optimizing the geometry of the parametric joint-confidence regions (CRs), which are obtained in an a posteriori analysis of the least-squares parameter estimates. The optimal design is achieved by using the a…
We propose a unified framework to address a family of classical mixed-integer optimization problems with logically constrained decision variables, including network design, facility location, unit commitment, sparse portfolio selection, binary quadratic optimization, sparse principal analysis and sparse learning proble…
We develop methods to learn dictionaries invariant under group symmetries, useful in cryo-EM and tracking.
problem Learning dictionaries invariant under group symmetries.
method Representation theory, non-abelian Fourier analysis, matrix orbitopes, alternating minimization.
result Effective dictionary learning for SO(3) symmetries with guarantees.
Develops a category-theoretic approach to interpret conformal prediction.
problem Interpreting conformal prediction as a quantitative uncertainty tool.
method Category-theoretic approach to represent and decompose conformal prediction.
result Decomposes conformal prediction into two steps: predictive distributions and prediction regions.
Examines algorithmic modeling across three cultures.
problem Tackles algorithmic modeling in different cultural contexts.
method Uses parametric regressions, interpretable algorithms, and complex algorithms.
result Extension of Leo Breiman's thesis to include cultural differences.
Playing repeated matrix games (RMG) while maximizing the cumulative returns is a basic method to evaluate multi-agent learning (MAL) algorithms. Previous work has shown that , , or algorithms have good behaviours on average in RMG. Besides, hedging algorithms have been shown to be effective on predi…
Meta-algorithm selection aims to choose the best algorithm selector for a given problem instance.
problem Selecting the best algorithm selector for a specific problem instance.
method Apply algorithm selection to the selection of other algorithms (meta-algorithm selection).
result Meta-algorithm selection can be beneficial in some cases but faces challenges in solving the meta-level problem.
Proposes CLRS benchmark to evaluate algorithmic reasoning.
problem Difficulty in transferring results across publications due to targeted algorithmic data.
method Develops a comprehensive benchmark covering various algorithmic tasks.
result Demonstrates performance of algorithmic reasoning baselines on the CLRS benchmark.
Combines multiple bandit algorithms to create a nearly optimal single algorithm.
problem Designing a single bandit algorithm that performs nearly as well as the best individual algorithm in a stochastic environment.
method Develops two general corralling algorithms that achieve favorable regret guarantees.
result The regret of the corralling algorithms is no worse than the best individual algorithm's performance.
Accelerated Randomized Coordinate Descent Algorithms for Stochastic Optimization and Online Learningcs.LG
We propose accelerated randomized coordinate descent algorithms for stochastic optimization and online learning. Our algorithms have significantly less per-iteration complexity than the known accelerated gradient algorithms. The proposed algorithms for online learning have better regret performance than the known rando…
The exchange algorithm is studied for its convergence and asymptotic variance.
problem Theoretical limitations of the exchange algorithm in sampling from doubly-intractable distributions.
method Theoretical analysis of the exchange algorithm's convergence speed and asymptotic variance.
result The exchange algorithm converges at a geometric rate and satisfies a Central Limit Theorem.
Bayesian networks (BN) are used in a big range of applications but they have one issue concerning parameter learning. In real application, training data are always incomplete or some nodes are hidden. To deal with this problem many learning parameter algorithms are suggested foreground EM, Gibbs sampling and RBE algori…
No algorithm outperforms uniform sampling in A/B testing.
problem Identifying the best arm in A/B testing with fixed budget.
method Introducing consistent and stable algorithms, deriving lower bounds, and proving optimality of uniform sampling.
result No algorithm performs better than uniform sampling in A/B testing.
This review article surveys data augmentation MCMC algorithms.
problem Sampling from intractable probability distributions.
method Comprehensive study of DA MCMC algorithms, their convergence properties, and acceleration strategies.
result Synthesizes recent developments and provides insights for researchers.
The Bayesian Learning Rulestat.ML
Bayesian learning rule unifies and generalizes various machine learning algorithms.
problem Machine learning algorithms are diverse and not always understood.
method Bayesian principles and natural gradients are used to derive algorithms.
result Derives a wide range of algorithms including classical and modern ones.
Learning to Optimizecs.LG
Algorithm design is a laborious process and often requires many iterations of ideation and validation. In this paper, we explore automating algorithm design and present a method to learn an optimization algorithm, which we believe to be the first method that can automatically discover a better algorithm. We approach th…
This review summarizes five Lasso optimization algorithms.
problem Optimizing the Lasso objective function.
method Five representative algorithms: ISTA, FISTA, CGDA, SLA, PFA.
result Comparison of convergence rates and strengths/weaknesses.
Neural networks mimic algorithms to solve complex problems.
problem Current machine learning methods struggle with generalisation and efficiency.
method Representing algorithms in a continuous space and adapting them to real-world problems.
result Neural networks can execute classical algorithms more efficiently.
Paper proposes a reinforcement learning framework for efficient hyper-parameter tuning of stochastic optimization algorithms.
problem Efficient tuning of hyper-parameters for stochastic optimization algorithms.
method Modeling hyper-parameter tuning as a Markov decision process and using policy gradient algorithms.
result The proposed framework significantly reduces the time required for hyper-parameter tuning compared to Bayesian optimization.
In this paper, we propose a convergent parallel best-response algorithm with the exact line search for the nondifferentiable nonconvex sparsity-regularized rank minimization problem. On the one hand, it exhibits a faster convergence than subgradient algorithms and block coordinate descent algorithms. On the other hand,…
Approximate probabilistic inference algorithms are central to many fields. Examples include sequential Monte Carlo inference in robotics, variational inference in machine learning, and Markov chain Monte Carlo inference in statistics. A key problem faced by practitioners is measuring the accuracy of an approximate infe…
New algorithms reduce bilevel optimization complexity to ε^(-1.5).
problem Efficiently solving bilevel optimization problems in machine learning.
method Proposed two new algorithms: one using momentum-based recursive iterations, the other using recursive gradient estimations.
result Achieved computational complexity of ε^(-1.5), significantly faster than previous methods.
The inverse-free extreme learning machine (ELM) algorithm proposed in [4] was based on an inverse-free algorithm to compute the regularized pseudo-inverse, which was deduced from an inverse-free recursive algorithm to update the inverse of a Hermitian matrix. Before that recursive algorithm was applied in [4], its impr…
Researchers analyze how algorithmic and implementation choices affect RL performance.
problem Difficulty in separating algorithmic and implementation differences in RL performance.
method Unified derivations through a single control-as-inference objective, categorizing algorithms as EM or KL minimization.
result Implementation details are co-adapted with algorithmic choices, some transferable across algorithms.
Study on selecting between base algorithms in stochastic bandit problems.
problem Model selection in stochastic environments with contextual information.
method Developed a meta-algorithm-base algorithm abstraction with a smoothing transformation for optimal guarantees.
result Optimal model selection guarantees for stochastic contextual bandit problems.
New bounds derived for KG algorithm's performance in finite time.
problem Best arm identification problem in multi-armed bandit.
method Theoretical analysis of finite-time performance, deriving bounds for sample allocation, error probability, and regret.
result Upper and lower bounds for the probability of error and simple regret of the KG algorithm.
Paper proves linear convergence of SCMS algorithm for directional data.
problem Identifying density ridges in directional data.
method Generalized SCMS algorithm to directional data, derived from SCGA with adaptive step size.
result Linear convergence of the proposed directional SCMS algorithm.
We resolve the fundamental problem of online decoding with general order ergodic Markov chain models. Specifically, we provide deterministic and randomized algorithms whose performance is close to that of the optimal offline algorithm even when latency is small. Our algorithms admit efficient implementation vi…
MLE and CVE are equivalent under exponential families, leading to faster and more stable EM algorithms.
problem Finding maximum likelihood estimators (MLE) efficiently and stably.
method Proved equivalence between MLE and CVE under exponential families, leading to an EM algorithm.
result EM algorithm achieves the same asymptotic variance as MLE and is faster and more stable.
New algorithm speeds up learning of graphical models.
problem Learning graphical models with sparse structure efficiently.
method Vertex-greedy score-based algorithm for learning DAGs.
result Polynomial runtime for learning DAG models.
The goal of data-driven algorithm design is to obtain high-performing algorithms for specific application domains using machine learning and data. Across many fields in AI, science, and engineering, practitioners will often fix a family of parameterized algorithms and then optimize those parameters to obtain good perfo…
The paper examines how algorithmic classification affects behavior and proposes democratizing stakes to mitigate predatory practices.
problem The impact of algorithmic classification on individual behavior and fairness in decision-making processes.
method Characterization of optimal classification by an algorithm designer and analysis of the effect of democratizing stakes.
result Optimal classification can lead to surprising behavior patterns, and democratizing stakes can mitigate predatory practices.
Run2Survive uses survival analysis for algorithm selection, outperforming traditional methods.
problem Handling censored runtime data in algorithm selection.
method Decision-theoretic approach leveraging survival analysis for censored data.
result Run2Survive outperforms state-of-the-art AS approaches in experiments.
IRT improves algorithm evaluation across datasets.
problem Evaluating the performance of algorithm portfolios.
method Modified IRT framework for evaluating algorithm portfolios across datasets.
result Richer characteristics of algorithm performance are revealed.
New algorithms improve machine learning performance with explicit regret bounds.
problem Improving machine learning performance with explicit regret bounds.
method Projection-based linear regression algorithms with a focus on modern machine-learning models and their algorithmic performance.
result Established a priori regret bounds with explicit λ-dependence.
The Kaczmarz algorithm is popular for iteratively solving an overdetermined system of linear equations. The traditional Kaczmarz algorithm can approximate the solution in few sweeps through the equations but a randomized version of the Kaczmarz algorithm was shown to converge exponentially and independent of number of …
The book explores alternatives to worst-case analysis for algorithm performance.
problem Providing strong worst-case guarantees for many algorithms is impossible.
method Surveying and detailing various nuanced analysis approaches.
result More nuanced analysis approaches are needed for fundamental problems.