We introduce a method that uses the Cauchy-Crofton formula and a new curvature formula from integral geometry to reweight the sampling probabilities of Metropolis-within-Gibbs algorithms in order to increase their convergence speed. We consider algorithms that sample from a probability density conditioned on a manifold…
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48 results for “subspace search”
This letter presents a new spectral-clustering-based approach to the subspace clustering problem. Underpinning the proposed method is a convex program for optimal direction search, which for each data point d finds an optimal direction in the span of the data that has minimum projection on the other data points and non…
AdaSub optimizes with second-order info in low-dims subspace.
problem Efficiently use second-order optimization methods with low computational cost.
method Adaptive subspace selection for second-order optimization.
result AdaSub outperforms other stochastic optimizers in time and iterations.
This paper introduces a simple and efficient density estimator that enables fast systematic search. To show its advantage over commonly used kernel density estimator, we apply it to outlying aspects mining. Outlying aspects mining discovers feature subsets (or subspaces) that describe how a query stand out from a given…
Subspace clustering aims to find groups of similar objects (clusters) that exist in lower dimensional subspaces from a high dimensional dataset. It has a wide range of applications, such as analysing high dimensional sensor data or DNA sequences. However, existing algorithms have limitations in finding clusters in non-…
The paper proves symplectic neighbourhood theorems for stratified subspaces.
problem Finding symplectic neighbourhoods of stratified subspaces.
method Analogy with Weinstein's neighbourhood theorem, strong version of Moser's trick, and tubular neighbourhood theorem.
result Generalization of existing constructions for exotic Lagrangians.
Motivated by vision tasks such as robust face and object recognition, we consider the following general problem: given a collection of low-dimensional linear subspaces in a high-dimensional ambient (image) space, and a query point (image), efficiently determine the nearest subspace to the query in distance. In…
New method reduces high-dimensional data to key features.
problem Challenges of high-dimensional data analysis and interpretability.
method Randomized search to produce subspaces, ensemble of models for variable selection.
result Outperforms existing methods in prediction and variable selection.
A new score SiNNE improves OAM efficiency and accuracy.
problem Comparing outlier scores across subspaces of different dimensions.
method Introducing SiNNE, a new score independent of subspace dimensionality.
result SiNNE produces better or at least as good results as existing scores and significantly improves runtime.
Sequential Subspace Search for Functional Bayesian Optimization Incorporating Experimenter Intuitioncs.LG
Bayesian optimization guided by experimenter intuition and beliefs.
problem Finding optimal functions with experimenter's beliefs incorporated.
method Sequential Subspace Search using Gaussian Process.
result Algorithm converges in sub-linear time with finite effective dimension.
Motivated by vision tasks such as robust face and object recognition, we consider the following general problem: given a collection of low-dimensional linear subspaces in a high-dimensional ambient (image) space and a query point (image), efficiently determine the nearest subspace to the query in distance. We …
Subspace Determination through Local Intrinsic Dimensional Decomposition: Theory and Experimentationcs.LG
Axis-aligned subspace clustering generally entails searching through enormous numbers of subspaces (feature combinations) and evaluation of cluster quality within each subspace. In this paper, we tackle the problem of identifying subsets of features with the most significant contribution to the formation of the local n…
Scaling Bayesian optimisation (BO) to high-dimensional search spaces is a active and open research problems particularly when no assumptions are made on function structure. The main reason is that at each iteration, BO requires to find global maximisation of acquisition function, which itself is a non-convex optimizati…
In subspace clustering, a group of data points belonging to a union of subspaces are assigned membership to their respective subspaces. This paper presents a new approach dubbed Innovation Pursuit (iPursuit) to the problem of subspace clustering using a new geometrical idea whereby subspaces are identified based on the…
Agents collaborate to reduce regret in a multi-agent linear bandit problem with side information.
problem Reducing regret in a multi-agent stochastic linear bandit with side information.
method A decentralized algorithm where agents communicate subspace indices and each plays a projected LinUCB on the corresponding low-dimensional subspace.
result Per-agent finite-time regret is much smaller when agents communicate compared to non-communicating case.
FiGS searches over a larger space of architectures for efficient mobile models.
problem Designing small, efficient deep networks for mobile devices.
method Differentiable search method using sparse regularization and Logistic-Sigmoid distribution.
result FiGS produces state-of-the-art parameter-efficient models on ImageNet and improves object detection performance.
Many applications in machine learning require optimizing a function whose true gradient is unknown, but where surrogate gradient information (directions that may be correlated with, but not necessarily identical to, the true gradient) is available instead. This arises when an approximate gradient is easier to compute t…
We propose a quantization based approach for fast approximate Maximum Inner Product Search (MIPS). Each database vector is quantized in multiple subspaces via a set of codebooks, learned directly by minimizing the inner product quantization error. Then, the inner product of a query to a database vector is approximated …
On the exact minimization of saturated loss functions for robust regression and subspace estimationcs.LG
This paper deals with robust regression and subspace estimation and more precisely with the problem of minimizing a saturated loss function. In particular, we focus on computational complexity issues and show that an exact algorithm with polynomial time-complexity with respect to the number of data can be devised for r…
Study optimizes solving fixed-point equations using subspace search.
problem Solving linear fixed point equations in Hilbert spaces.
method Linear stochastic approximation scheme with Polyak--Ruppert averaging.
result Established optimal approximation factor for temporal difference learning methods.
The idea of Innovation Search was proposed as a data clustering method in which the directions of innovation were utilized to compute the adjacency matrix and it was shown that Innovation Pursuit can notably outperform the self representation based subspace clustering methods. In this paper, we present a new discovery …
In several application domains, high-dimensional observations are collected and then analysed in search for naturally occurring data clusters which might provide further insights about the nature of the problem. In this paper we describe a new approach for partitioning such high-dimensional data. Our assumption is that…
Neural Architecture Search (NAS) is an emerging topic in machine learning and computer vision. The fundamental ideology of NAS is using an automatic mechanism to replace manual designs for exploring powerful network architectures. One of the key factors of NAS is to scale-up the search space, e.g., increasing the numbe…
In this paper, we propose a successive convex approximation framework for sparse optimization where the nonsmooth regularization function in the objective function is nonconvex and it can be written as the difference of two convex functions. The proposed framework is based on a nontrivial combination of the majorizatio…
In this paper, we propose a novel lower dimensional representation of a shape sequence. The proposed dimension reduction is invertible and computationally more efficient in comparison to other related works. Theoretically, the differential geometry tools such as moving frame and parallel transportation are successfully…
Proposes a method to reveal nonlinearities in tensor data.
problem Capturing nonlinear relationships in high-dimensional tensor data.
method Linear tensor projection method to maximize prediction accuracy.
result Effective in revealing nonlinear relationships in tensor data.
Visual reranking is effective to improve the performance of the text-based video search. However, existing reranking algorithms can only achieve limited improvement because of the well-known semantic gap between low level visual features and high level semantic concepts. In this paper, we adopt interactive video search…
AMEIR automates recommender system design using NAS.
problem Manual feature and architecture engineering in recommender systems.
method Three-stage search space and tailored three-step pipeline.
result AMEIR outperforms manual and complex NAS methods.
BAxUS optimizes high-dimensional functions adaptively, avoiding performance degradation and failure.
problem State-of-the-art HDBO methods degrade or fail with increasing dimensions.
method BAxUS uses nested random subspaces to adaptively optimize high-dimensional functions.
result BAxUS outperforms state-of-the-art methods across various applications.
The paper finds non-Gaussian directions in high-dimensional data using Wasserstein distance.
problem Locating interesting non-Gaussian features in high-dimensional data.
method Projection pursuit using 2-Wasserstein distance to maximize the difference from Gaussian.
result Statistical guarantees for accurately approximating an unknown low-dimensional non-Gaussian subspace.
We propose a general technique for improving alternating optimization (AO) of nonconvex functions. Starting from the solution given by AO, we conduct another sequence of searches over subspaces that are both meaningful to the optimization problem at hand and different from those used by AO. To demonstrate the utility o…
Robust principal component analysis (RPCA) can recover low-rank matrices when they are corrupted by sparse noises. In practice, many matrices are, however, of high-rank and hence cannot be recovered by RPCA. We propose a novel method called robust kernel principal component analysis (RKPCA) to decompose a partially cor…
Paper proposes a new approach to Model Selection using a U-curve algorithm.
problem Model Selection in Machine Learning.
method Data-driven, non-exhaustive search of a Learning Space .
result Conditions for non-exhaustive search to return optimal solutions.
We consider the task of learning the parameters of a {\em single} component of a mixture model, for the case when we are given {\em side information} about that component, we call this the "search problem" in mixture models. We would like to solve this with computational and sample complexity lower than solving the ove…
A new method routes EEG covariance matrices across domains using adaptive subspace selection.
problem Challenges in cross-domain EEG decoding due to distinct SPD manifold regions.
method Dynamic Stiefel routing with expert filters and cross-attention for adaptive subspace projection.
result Consistent gains across three datasets: balanced accuracy improves from 0.773 to 0.823, 0.757 to 0.809, and 0.801 to 0.839.
Efficient method for generating adversarial examples with limited query budget.
problem Developing black-box adversarial attacks with limited information.
method Bayesian Optimization in a structured low-dimensional subspace.
result Significantly higher attack success rate with fewer queries.
Bayesian optimization is known to be difficult to scale to high dimensions, because the acquisition step requires solving a non-convex optimization problem in the same search space. In order to scale the method and keep its benefits, we propose an algorithm (LineBO) that restricts the problem to a sequence of iterative…
Improved genetic programming by optimizing mutation operators for continuous program search.
problem Small syntactic mutations in genetic programming can lead to unpredictable behavioral shifts.
method Learned a compact trading-strategy DSL, created a block-factorized embedding, and designed geometry-compiled mutation operators.
result Geometry-compiled mutation operators discover strong strategies using fewer evaluations and achieve higher Sharpe ratios.
The recent developments of basis pursuit and compressed sensing seek to extract information from as few samples as possible. In such applications, since the number of samples is restricted, one should deploy the sampling points wisely. We are motivated to study the optimal distribution of finite sampling points. Formul…
A theory of sufficient dimension reduction (SDR) is developed from an optimizational perspective. In our formulation of the problem, instead of dealing with raw data, we assume that our ground truth includes a mapping and a probability distribution function over…
pPCA speeds up PCA by priming initial estimates for faster, more accurate results.
problem Improving the speed and accuracy of principal component analysis (PCA).
method pPCA is a two-step algorithm: first, an approximate-PCA method primes the data, then exact PCA is applied in the span of the initial estimate.
result pPCA improves accuracy significantly with a small computational cost, outperforming other methods across various datasets.
Hashing techniques have been applied broadly in retrieval tasks due to their low storage requirements and high speed of processing. Many hashing methods based on a single view have been extensively studied for information retrieval. However, the representation capacity of a single view is insufficient and some discrimi…
AI-driven framework optimizes MCMC-based preconditioners for faster linear system solving.
problem Slow convergence of Krylov subspace solvers for ill-conditioned matrices.
method Graph neural surrogate and Bayesian optimization for AI-tuned MCMC parameters.
result 50% reduction in iterations to convergence on unseen system.
New algorithms optimize faster for simpler problems in machine learning.
problem Design faster optimization algorithms for practical machine learning problems.
method Adaptive gradient algorithms with refined conditions based on Hessian singular values.
result Achieved optimal gradient complexity for linear regression.
Paper bounds subspace estimator error from noisy projections.
problem Estimating subspaces from noisy data.
method Derives perturbation bound on optimal subspace estimator.
result Fundamental result with implications in matrix completion and clustering.
PCA is one of the most widely used dimension reduction techniques. A related easier problem is "subspace learning" or "subspace estimation". Given relatively clean data, both are easily solved via singular value decomposition (SVD). The problem of subspace learning or PCA in the presence of outliers is called robust su…
Union of Subspaces (UoS) is a popular model to describe the underlying low-dimensional structure of data. The fine details of UoS structure can be described in terms of canonical angles (also known as principal angles) between subspaces, which is a well-known characterization for relative subspace positions. In this pa…
Study -orbits in complex and -complex subspaces of Hermitian quaternionic vector spaces.
problem Characterize -orbits in Grassmannians of complex and -complex subspaces.
method Decompose subspaces into 4-dimensional complex addends and 2-dimensional totally complex subspace. Use properties of isoclinic subspaces and principal angles.
result Determine full set of invariants for -orbits in .