Parsimonious Dynamic Mode Decomposition selects sparse modes robustly.
problem Manual tuning of sparsity parameters in traditional DMD.
method Time-delay embedding and Orthogonal Matching Pursuit.
result Autonomously determines optimally sparse subset of modes.
New method decomposes KL error using refined information and mode interactions.
problem Learning probability distributions over discrete variables with higher-order interactions.
method Using information geometry, refined mode interactions, and a novel Monte-Carlo sampling technique.
result Complete decomposition of KL error and efficient data use.
Sparse-mode DMD disambiguates local and global modes in spatiotemporal data.
problem Disambiguating local and global modes in spatiotemporal data.
method Sparse-mode DMD with sparsity-promoting regularization.
result Explicitly constructs discrete and continuous spectra.
The paper improves GP regression for sparse sensor data in structural mode shape reconstruction.
problem Reconstructing full-field structural mode shapes from sparse sensor data.
method Physics-Constrained Single-Output Gaussian Process (CONS-SOGP) framework.
result The proposed method provides more accurate and reliable mode shapes.
SRMD uses random features for efficient time-frequency analysis.
problem Efficiently analyzing time-series data with low computational cost.
method Sparse Random Mode Decomposition (SRMD) constructs a sparse approximation to the spectrogram.
result SRMD outperforms other methods in signal representation, outlier removal, and mode decomposition.
New method uses random projections to estimate densities and modes efficiently.
problem Estimating densities and modes from sparse representations.
method Expand-and-sparsify representations followed by linear function and mode recovery algorithms.
result Optimal rates for density and mode estimation achieved.
In this article, we propose a new class of priors for Bayesian inference with multiple Gaussian graphical models. We introduce fully Bayesian treatments of two popular procedures, the group graphical lasso and the fused graphical lasso, and extend them to a continuous spike-and-slab framework to allow self-adaptive shr…
Dynamic Mode Decomposition (DMD) yields a linear, approximate model of a system's dynamics that is built from data. We seek to reduce the order of this model by identifying a reduced set of modes that best fit the output. We adopt a model selection algorithm from statistics and machine learning known as Least Angle Reg…
Improved Bayesian neural network inference by selectively removing redundant modes.
problem Redundant modes in Bayesian neural network posteriors complicate approximate inference.
method Structured partial stochasticity and deterministic subset selection of weights.
result Improved performance of approximate inference schemes with simplified posterior distribution.
Framework predicts remaining useful life of DSH subsystems under unknown failure modes.
problem Predicting remaining useful life of DSH subsystems with unknown failure modes.
method Unsupervised framework using mixture of Gaussian regressions and Expectation-Maximization algorithm.
result Improved prediction accuracy and interpretability of RUL.
We consider N-way data arrays and low-rank tensor factorizations where the time mode is coded as a sparse linear combination of temporal elements from an over-complete library. Our method, Shape Constrained Tensor Decomposition (SCTD) is based upon the CANDECOMP/PARAFAC (CP) decomposition which produces r-rank appr…
We present a nonparametric method for selecting informative features in high-dimensional clustering problems. We start with a screening step that uses a test for multimodality. Then we apply kernel density estimation and mode clustering to the selected features. The output of the method consists of a list of relevant f…
Solving tasks with sparse rewards is one of the most important challenges in reinforcement learning. In the single-agent setting, this challenge is addressed by introducing intrinsic rewards that motivate agents to explore unseen regions of their state spaces; however, applying these techniques naively to the multi-age…
The paper evaluates samplers on multi-modal targets, focusing on mode separation and recovery.
problem Handling multi-modality in sampling.
method Synthetic experimental setting focusing on mode relative importance recovery.
result Illustrates the challenges and potential of samplers in multi-modality.
Physics-informed GCRL tackles sparse feedback learning with hybrid dynamics.
problem Sparse feedback learning with high-dimensional, hybrid, or contact-dependent dynamics.
method Introduces physics-informed inductive biases into goal-conditioned value learning.
result Contact-rich manipulation tasks degrade existing Pi-GCRL methods.
Many problems of low-level computer vision and image processing, such as denoising, deconvolution, tomographic reconstruction or super-resolution, can be addressed by maximizing the posterior distribution of a sparse linear model (SLM). We show how higher-order Bayesian decision-making problems, such as optimizing imag…
Bayesian system ID improves robustness to sparse, noisy data.
problem Robust system identification with sparse, noisy data.
method Probabilistic formulation of system identification using Bayesian posterior.
result The log posterior is more robust and less affected by multiple minima.
ERDMD discovers sparse, nonuniformly timed DMD models from chaotic attractors.
problem Discovering high-fidelity, nonuniformly timed DMD models from chaotic data.
method Entropic regression for nonlinear information flow detection, combined with multi-step DMD.
result ERDMD produces highly efficient and robust models with minimal complexity.
Transformers excel at sparse token selection, surpassing FCNs in both worst and average cases.
problem Sparse token selection task
method One-layer transformer trained with gradient descent
result Transformers learn sparse token selection and exhibit strong out-of-distribution length generalization
VINNAS uses variational inference to avoid mode collapse in neural architecture search.
problem Mode collapse in gradient-based NAS methods, leading to suboptimal architectures.
method Differentiable variational inference with variational dropout and automatic relevance determination.
result State-of-the-art accuracy with up to twice fewer non-zero parameters.
Sparse PCA selects variables with FDR control for improved performance.
problem Sparse PCA selects irrelevant variables when maximizing explained variance.
method Proposes FDR-controlled selection using T-Rex selector.
result Significant performance improvement over traditional sparse PCA.
Sparse GEMINI selects relevant features for clustering without assumptions.
problem Feature selection in clustering with relevant clusters and variables.
method Discriminative clustering model maximizing GEMINI with l1 penalty.
result Sparse GEMINI selects relevant subsets of variables without prior hypotheses.
Efficiently selects predictors in sparse regression without approximations.
problem High computational cost in subset selection for sparse regression.
method Conditional uncorrelation formula and efficient non-approximate method.
result Significant reduction in computational complexity for subset selection.
Revisits online Laplace methods for neural networks, showing they are sound under certain conditions.
problem Online Laplace methods violate the Laplace approximation's critical assumption.
method Re-derives online Laplace methods, showing they target a variational bound on a mode-corrected variant of the Laplace evidence.
result Online Laplace and its mode-corrected counterpart share stationary points that satisfy the Laplace method's assumption.
The paper uses TDA to select stocks for a sparse portfolio, improving performance across market scenarios.
problem Sparse portfolio selection in financial markets.
method Topological data analysis (TDA) for clustering stock price movements.
result The TDA-based clustering strategy significantly enhances sparse portfolio performance.
Method learns hierarchical representations of samples and features simultaneously.
problem Hierarchical structures in samples and features not considered by existing methods.
method Jointly learns hierarchical representations via Tree-Wasserstein Distance alternating between samples and features.
result Method improves performance in link prediction and node classification tasks.
A framework selects GANs for specific applications efficiently.
problem Fragmented knowledge leads to trial-error selection of GANs.
method Comprehensive summary of GANs, comparison, and novel framework.
result Significant reduction in search space for GAN selection.
A new knot selection method speeds up sparse Gaussian process approximations.
problem Efficiently selecting knots for sparse Gaussian processes.
method One-at-a-time Bayesian optimization for knot selection.
result Competitive performance with reduced computational cost.
New metrics improve scRNA-seq perturbation modeling by reducing mode collapse.
problem Outperformed by simple mean prediction in scRNA-seq perturbation modeling.
method Introduce DEG-aware metrics (WMSE, Rw2(Δ)) and negative/positive baselines. result WMSE loss function reduces mode collapse and improves model performance.
Bayesian taut splines estimate modes in probability densities.
problem Estimating the number of modes in probability density functions.
method Bayesian inference with flexible kernel estimators and compositional splines.
result The new method provides more accurate results than traditional approaches.
sgboost reduces variable selection bias in boosting with balanced group selection.
problem Reduces variable selection bias in boosting algorithms.
method Simulation-based approach to balance selection frequencies of base-learners.
result Demonstrates efficacy through simulations and flexible group variable selection.
Sparse feature selection has been demonstrated to be effective in handling high-dimensional data. While promising, most of the existing works use convex methods, which may be suboptimal in terms of the accuracy of feature selection and parameter estimation. In this paper, we expand a nonconvex paradigm to sparse group …
We consider the problem of learning from sparse and underspecified rewards, where an agent receives a complex input, such as a natural language instruction, and needs to generate a complex response, such as an action sequence, while only receiving binary success-failure feedback. Such success-failure rewards are often …
OOMP selects features online for sparse linear regression.
problem Feature selection in high-dimensional sparse linear models.
method Online algorithm that alternates between feature selection and coefficient estimation.
result Theoretical guarantees and computational complexity analysis of OOMP.
LLMs learn to recommend models and hyperparameters from dataset metadata.
problem Model and hyperparameter selection in machine learning is challenging and resource-intensive.
method Converted datasets into metadata and prompted LLMs to recommend models and hyperparameters.
result LLMs can recommend competitive models and hyperparameters without search.
A new method selects features efficiently for high-dimensional data.
problem High computational costs and memory requirements in high-dimensional data.
method QuickSelection uses the strength of neurons in sparse autoencoders to select features.
result QuickSelection achieves the best trade-off of accuracy, speed, and memory usage.
MMCGAN uses explicit manifold learning to improve GAN performance.
problem GAN mode collapse and unstable training.
method Introduces Minimum Manifold Coding (MMC) as a prior to guide GAN training.
result MMCGAN effectively alleviates mode collapse and stabilizes GAN training.
Many complex dynamical phenomena can be effectively modeled by a system that switches among a set of conditionally linear dynamical modes. We consider two such models: the switching linear dynamical system (SLDS) and the switching vector autoregressive (VAR) process. Our Bayesian nonparametric approach utilizes a hiera…
In this paper, we propose ℓp-norm regularized models to seek near-optimal sparse portfolios. These sparse solutions reduce the complexity of portfolio implementation and management. Theoretical results are established to guarantee the sparsity of the second-order KKT points of the ℓp-norm regularized models…
New method for k-modes algorithm improves clustering performance.
problem Improving initial solution selection for k-modes algorithm.
method Uses Hospital-Resident Assignment Problem to find initial cluster centroids.
result Outperforms other initialisations in most cases, especially for low-density data.
A scalable gradient-based framework for sparse portfolio selection.
problem Sparse minimum-variance portfolio selection with cardinality constraint.
method Gradient-based optimization with Boolean relaxation and tunable parameter.
result Matches commercial solvers in most instances, differing by a few assets with negligible error in portfolio variance.
We propose a K-sparse exhaustive search (ES-K) method and a K-sparse approximate exhaustive search method (AES-K) for selecting variables in linear regression. With these methods, K-sparse combinations of variables are tested exhaustively assuming that the optimal combination of explanatory variables is K-sparse. By co…
Mixed membership factorization is a popular approach for analyzing data sets that have within-sample heterogeneity. In recent years, several algorithms have been developed for mixed membership matrix factorization, but they only guarantee estimates from a local optimum. Here, we derive a global optimization (GOP) algor…
Paper introduces DP methods for high-dimensional variable selection.
problem Sparse variable selection in high-dimensional learning.
method Pure differentially private estimators using Integer Programming.
result Achieves state-of-the-art empirical support recovery.
Improves Group Lasso for categorical data by reducing dimensionality and selecting models.
problem Sparse modelling of categorical data is challenging, especially for high dimensions.
method Two-step procedure: first, reduce dimensionality using Group Lasso; second, select final model using an information criterion on clustered levels.
result The method produces a sparse solution and performs better than state-of-the-art algorithms in prediction accuracy and model dimension.
Develops methods for selecting and estimating smooth functional coefficients in high-dimensional multivariate functional data.
problem Functional predictor selection and estimation of smooth functional coefficients in high-dimensional multivariate functional data.
method Functional group-sparse regression methods in a generic Hilbert space of infinite dimension.
result Consistency of estimation and selection (oracle property) under infinite-dimensional Hilbert spaces.
Proposes a Bayesian approach for automatic node selection in sparse neural networks.
problem Reduces structural complexity and computational speedup in large-scale predictive models.
method Uses spike-and-slab Gaussian priors and variational Bayes approach for node selection.
result Establishes variational posterior consistency and optimal contraction rates for sparse networks.
Proposes a more efficient knot selection method for sparse Gaussian processes.
problem Optimizing marginal likelihood for knot selection leads to suboptimal and inefficient placement of knots.
method Uses Bayesian optimization to propose knots one at a time, avoiding multimodal surface issues.
result Improves both accuracy and speed of knot selection compared to current methods.