Random feature maps improve forecasting with cheaper computation.
problem Improving forecasting accuracy with random feature maps.
method Developed a hit-and-run algorithm to select optimal internal weights.
result Optimal internal weights lead to superior forecasting skill.
We analyze random feature maps for high-dimensional data using spectral methods.
problem Understanding the spectrum of random feature maps for high-dimensional data.
method We use concentration phenomena from random matrix theory to analyze the Gram matrix of random feature maps for Gaussian mixture models.
result Our results provide insights into the interplay between nonlinearity and data statistics.
Random feature maps improve forecasting of chaotic dynamical systems.
problem Forecasting chaotic dynamical systems with high accuracy.
method Data-driven random feature maps with tanh activation, skip connections, and localization.
result Effective forecasting skill for dynamical systems with dimensions up to 512.
RFSVM with random features achieves faster learning rates.
problem Improving the learning rate of SVM with random features.
method Support Vector Machine with N ≪ m N\ll m N ≪ m random features, optimized feature map, and reweighted feature selection. result RFSVM achieves faster learning rates than O ( 1 / m ) O(1/\sqrt{m}) O ( 1/ m ) under low noise assumptions. Paper explores Polya's characterization of positive-definite kernels and random feature maps.
problem Characterizing positive-definite kernels and their random feature maps.
method Study Polya's criterion and derive novel kernels; compare random Fourier and binning feature maps.
result Random binning feature map yields a closer Euclidean inner product to the kernel.
Lower bound proves ridgeless regression performs poorly near interpolation threshold.
problem Proving performance of ridgeless regression near interpolation threshold.
method Distribution-independent lower bound for mean squared error in noisy ridgeless linear regression.
result Lower bound implies ridgeless regression performs poorly near interpolation threshold.
New random feature maps for Laplacian and related kernels.
problem Challenges in approximating the Laplacian kernel and its generalizations.
method Developed random feature maps for Laplacian and related kernels, providing efficient sampling schemes.
result Demonstrated the efficacy of these random feature maps on real datasets.
Kernel approximation using randomized feature maps has recently gained a lot of interest. In this work, we identify that previous approaches for polynomial kernel approximation create maps that are rank deficient, and therefore do not utilize the capacity of the projected feature space effectively. To address this chal…
Generative model uses random convolutional features to create financial time series.
problem Generating realistic financial time series with limited data and avoiding overfitting.
method Train generators by matching random convolutional features of real and generated time series, using SOCK (SOft Competing Kernels) feature map.
result Generators trained with random SOCK features outperform baselines across various financial datasets.
Random feature model approximates PDE solutions efficiently.
problem Approximating solutions to PDEs with high-dimensional inputs and outputs.
method Random feature model applied to infinite-dimensional operators.
result Efficient and accurate approximation of PDE solutions.
We find a deterministic equivalent for random feature regression's test error, independent of feature map dimension.
problem Understanding the generalization performance of random feature ridge regression.
method We derive a deterministic equivalent for the test error of RFRR under a concentration property, showing it can be approximated by a closed-form expression dependent on feature map eigenvalues.
result Our approximation guarantee is non-asymptotic, multiplicative, and independent of the feature map dimension, providing a tight result for the smallest number of features achieving optimal minimax error rate.
Proposes a method for kernel learning using feature maps.
problem Improving SVM margin through iterative refinement.
method Fourier-analytic characterization and iterative feature maps.
result Optimal and generalization guarantees for SVM margin improvement.
Sensitivity Maps improve HSIC for better interpretability and scalability.
problem High computational cost and lack of interpretability in HSIC.
method Introduce Sensitivity Maps (SMs) for HSIC, approximate kernels using random features, and provide convergence bounds.
result RHSIC and SMs efficiently approximate HSIC and provide scalable solutions.
New bounds for RFM-KRR with weak assumptions and easy verification.
problem Establishing accurate out-of-sample bounds for RFM-KRR.
method Elementary linear algebra and weak assumptions.
result Novel out-of-sample error upper and lower bounds with weak assumptions.
Unified feature maps for graph kernels improve efficiency without sacrificing accuracy.
problem Efficiently applying non-linear kernel methods to large-scale graph data.
method Constructing feature maps for graph kernels, analyzing feasibility, and proposing algorithms.
result Explicit feature maps can achieve similar accuracy to kernel trick methods but with significantly reduced computation time.
LaRP framework improves object classification using random projections.
problem Efficiently approximating nonlinear kernels in high-dimensional spaces.
method Separates linear kernels and nonlinearity using a layered random projection approach.
result Notable improvement in object classification performance.
We analyze in this paper a random feature map based on a theory of invariance I-theory introduced recently. More specifically, a group invariant signal signature is obtained through cumulative distributions of group transformed random projections. Our analysis bridges invariant feature learning with kernel methods, as …
Recent years have demonstrated that using random feature maps can significantly decrease the training and testing times of kernel-based algorithms without significantly lowering their accuracy. Regrettably, because random features are target-agnostic, typically thousands of such features are necessary to achieve accept…
Efficiently applies NTK to large-scale datasets using random features.
problem Computational limitations of kernel methods for large-scale datasets.
method Proposes a sketching-based algorithm combining random features of arc-cosine kernels to construct an efficient feature map of the NTK.
result Achieves comparable error bounds to exact kernel methods but with significantly reduced feature dimensionality.
Approximating non-linear kernels using feature maps has gained a lot of interest in recent years due to applications in reducing training and testing times of SVM classifiers and other kernel based learning algorithms. We extend this line of work and present low distortion embeddings for dot product kernels into linear…
New method selects variables for nonlinear regression in large datasets.
problem Nonlinear regression with large-scale datasets.
method Kernel-based variable selection with random features.
result Outstanding performance on large-scale synthetic and real datasets.
Map matching of the GPS trajectory serves the purpose of recovering the original route on a road network from a sequence of noisy GPS observations. It is a fundamental technique to many Location Based Services. However, map matching of a low sampling rate on urban road network is still a challenging task. In this paper…
Characterizes test error in learning with deep, structured feature maps.
problem Characterizing test error in learning with deep, structured feature maps.
method Asymptotic analysis of feature covariance and population covariance.
result Closed-form formula for feature covariance in Gaussian rainbow neural networks.
New algorithms efficiently model nonlinear data without mapping to RKHS.
problem Nonlinear modeling in RKH spaces with computational efficiency.
method Use random Fourier features to map data to a finite Euclidean space, approximating kernel functions.
result Linear algorithms converge at similar speeds and error floors, with computational efficiency.
Proposes MGPLL for PL learning with non-random noise.
problem Partial label learning with non-random label noise.
method Bi-directional mapping framework, conditional noise label generation, multi-class predictor, adversarial learning.
result Demonstrates state-of-the-art performance in partial label learning.
A faster graph kernel using optical random features.
problem High computation cost of graphlet kernel due to isomorphism test.
method Kernel random features, optical random features, mean kernel metric.
result The proposed method is orders of magnitude faster with similar or better accuracy.
Paper introduces a method for operator learning using random features.
problem Estimating maps between infinite-dimensional spaces using input-output pairs.
method Function-valued random features method, building a linear combination of random operators.
result The method provides convergence guarantees and error bounds for nonlinear problems.
New method uses random features and Tikhonov regularization for operator learning from noisy data.
problem Accurate approximation of mappings between infinite-dimensional function spaces with reduced training time.
method Regularized random Fourier features (RRFF) coupled with finite element reconstruction (RRFF-FEM).
result The method achieves improved performance with reduced training time and noise robustness.
The paper compares Bayesian uncertainty to MAP estimator in random features regression.
problem Comparing Bayesian uncertainty to MAP estimator in random features regression.
method Analyzing the variance of the posterior predictive distribution and comparing it to the risk of the MAP estimator.
result Asymptotic agreement between Bayesian uncertainty and MAP estimator under specific signal-to-noise ratios and sample sizes.
New method improves kernel approximation for larger datasets.
problem Efficiently approximate kernel functions for large datasets.
method Monte Carlo integration for numerical approximation of kernel functions.
result Improved convergence behavior and empirical support for better kernel estimates.
Random ReLU features are shown to be a universally consistent learning algorithm but struggle with complex functions.
problem Approximating complex functions with random ReLU features.
method Study of random ReLU features through their RKHS and composition of functions.
result Random ReLU features can efficiently approximate complex functions but not as well as multi-layer ReLU networks.
A new method reduces the number of features needed for kernel approximation from cubic to logarithmic.
problem Large datasets make kernel methods computationally expensive and impractical.
method Combines random feature maps with data-dependent feature selection to achieve Nystrom-like performance with fewer features.
result Achieves small kernel matrix approximation error and better test set accuracy with fewer features than state-of-the-art methods.
Map matching of GPS trajectories from a sequence of noisy observations serves the purpose of recovering the original routes in a road network. In this work in progress, we attempt to share our experience of feature construction in a spatial database by reporting our ongoing experiment of feature extrac-tion in Conditio…
Random features and KRR generalize similarly when N is large enough.
problem Understanding the generalization error of random features and KRR methods.
method Analyzing spectral conditions and hypercontractivity on kernel eigenfunctions.
result The test error of random features is larger than KRR when N is small, but they achieve the same error when N is large.
No-trick kernel adaptive filtering uses deterministic features for scalability and robustness.
problem Scalability issues in kernel methods for large datasets.
method Deterministic feature-map construction using polynomial-exact solutions.
result Deterministic features outperform random Fourier features in performance and scalability.
Random Fourier features improve tabular deep learning convergence.
problem Tabular deep learning convergence issues.
method Random Fourier projections as a pre-processing step, projecting inputs into a fixed feature space.
result Random Fourier pre-processing accelerates tabular deep learning convergence.
Random Forest proximity distances reveal feature contributions in black-box models.
problem Understanding feature contributions in complex, opaque machine learning models.
method Observing changes in input affecting proximity distances and instance movement in decision space.
result Each feature's independent contribution to model decisions can be calculated and analyzed.
New method recovers sparse vectors from random sinusoidal features.
problem Recovering sparse vectors from random sinusoidal features.
method Proposes a numerically stable algorithm for sparse vector reconstruction.
result Sparse vectors can be reliably recovered from random sinusoidal features.
Space-efficient feature maps improve string alignment kernel scalability.
problem String alignment kernels scale poorly with quadratic complexity, limiting large-scale applications.
method Presented SFMEDM, a space-efficient feature map for edit distance with moves using metric embedding and random Fourier features.
result Demonstrated superior performance of SFMEDM in prediction accuracy, scalability, and computation efficiency.
We consider the problem of improving the efficiency of randomized Fourier feature maps to accelerate training and testing speed of kernel methods on large datasets. These approximate feature maps arise as Monte Carlo approximations to integral representations of shift-invariant kernel functions (e.g., Gaussian kernel).…
In this paper, we propose and study random maxout features, which are constructed by first projecting the input data onto sets of randomly generated vectors with Gaussian elements, and then outputing the maximum projection value for each set. We show that the resulting random feature map, when used in conjunction with …
Deep random feature models are analyzed for their performance with exact asymptotic expressions.
problem Understanding the performance of deep random feature models.
method Established a novel universality result and used the convex Gaussian Min-Max theorem.
result Exact asymptotic expressions for the performance of deep random feature models are derived.
Random feature models approximate functions in Banach spaces efficiently.
problem Approximating functions in Banach spaces efficiently.
method Randomly initialized feature maps and linear readout training.
result Universal approximation in Bochner spaces for Banach space-valued models.
End-to-end kernel learning using generative RFFs for improved performance.
problem Improving kernel learning performance and generalization.
method Develops a generative network via RFFs to implicitly learn the kernel, followed by a linear classifier, jointly trained by ERM.
result Shows superior generalization performance over classical methods in real-world tasks.
Framework combines random features with CDEs for efficient time-series learning.
problem Efficient training of time-series models with strong inductive bias.
method Random Fourier CDEs and Random Rough DEs using continuous-time reservoirs and log-ODE discretization.
result Unified perspective on random-feature reservoirs and path-signature theory.
Attention layers are sensitive to single words, improving generalization over random features.
problem Understanding why attention layers are effective in NLP tasks.
method Study of word sensitivity in random features using BERT-Base word embeddings.
result Attention layers have high word sensitivity, improving generalization over random features.
New string kernels discover global properties through random feature maps, avoiding quadratic complexity.
problem Existing string kernels struggle with capturing long patterns, maintaining positive definiteness, and handling large datasets efficiently.
method Proposes a new class of global string kernels using random feature maps to discover global properties through global alignments, ensuring positive definiteness and linear computational cost.
result Random String Embeddings (RSE) achieve better or comparable accuracy to state-of-the-art methods, especially for longer strings.
This paper uses PCA and FA for feature selection in credit rating.
problem Selecting important features for credit rating prediction.
method Principal Component Analysis and Factor Analysis.
result Factor Analysis reduces feature set significantly without losing much accuracy.