We consider partially observed multiscale diffusion models that are specified up to an unknown vector parameter. We establish for a very general class of test functions that the filter of the original model converges to a filter of reduced dimension. Then, this result is used to justify statistical estimation for the u…
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47 results for “reduced-dimension”
The Whitney embedding theorem gives an upper bound on the smallest embedding dimension of a manifold. If a data set lies on a manifold, a random projection into this reduced dimension will retain the manifold structure. Here we present an algorithm to find a projection that distorts the data as little as possible.
Study reduces dimensions for -means clustering for better accuracy.
problem Improving accuracy of -means clustering with high-dimensional data.
method Four randomized algorithms: two feature selection and two feature extraction.
result Provably accurate approximations of -means clustering are obtained.
In recent years, randomized methods for numerical linear algebra have received growing interest as a general approach to large-scale problems. Typically, the essential ingredient of these methods is some form of randomized dimension reduction, which accelerates computations, but also creates random approximation error.…
This paper evaluates t-SNE and MDS for reducing dimensions in datasets and classifying them with KNN, ENN, and SVM.
problem Reducing dimensions in datasets for better classification performance.
method t-SNE and MDS applied to nine datasets, followed by KNN, ENN, and SVM classification.
result Performance comparison of t-SNE and MDS with KNN, ENN, and SVM.
Space-time adaptive processing (STAP) algorithms with coprime arrays can provide good clutter suppression potential with low cost in airborne radar systems as compared with their uniform linear arrays counterparts. However, the performance of these algorithms is limited by the training samples support in practical appl…
SPreVcs.GR
SPREV simplifies visualization of complex labeled datasets.
problem Challenges of reducing dimensions and visualizing labeled datasets with small class size, high dimensionality, and low sample size.
method SPREV uses a novel dimensionality reduction technique integrating geometric principles.
result SPREV effectively visualizes hidden patterns in complex labeled datasets.
A Method of Reducing Dimension of Space Variables in Multi-dimensional Black-Scholes Equationsq-fin.CP
We study a method of reducing space dimension in multi-dimensional Black-Scholes partial differential equations as well as in multi-dimensional parabolic equations. We prove that a multiplicative transformation of space variables in the Black-Scholes partial differential equation reserves the form of Black-Scholes part…
Self-Organizing Maps (SOM) are popular unsupervised artificial neural network used to reduce dimensions and visualize data. Visual interpretation from Self-Organizing Maps (SOM) has been limited due to grid approach of data representation, which makes inter-scenario analysis impossible. The paper proposes a new way to …
End-to-end deep reinforcement learning has enabled agents to learn with little preprocessing by humans. However, it is still difficult to learn stably and efficiently because the learning method usually uses a nonlinear function approximation. Neural Episodic Control (NEC), which has been proposed in order to improve s…
Machine Learning models are vulnerable to adversarial attacks that rely on perturbing the input data. This work proposes a novel strategy using Autoencoder Deep Neural Networks to defend a machine learning model against two gradient-based attacks: The Fast Gradient Sign attack and Fast Gradient attack. First we use an …
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…
We discuss a general notion of "sparsity structure" and associated recoveries of a sparse signal from its linear image of reduced dimension possibly corrupted with noise. Our approach allows for unified treatment of (a) the "usual sparsity" and "usual recovery," (b) block-sparsity with possibly overlapping blo…
Standard methods for anomaly detection assume that all features are observed at both learning time and prediction time. Such methods cannot process data containing missing values. This paper studies five strategies for handling missing values in test queries: (a) mean imputation, (b) MAP imputation, (c) reduction (redu…
Paper reduces dimensionality for robust option pricing in 2-asset markets.
problem Robust option pricing in multi-asset markets with sub- or supermodular payoffs.
method Investigates the geometry of VMOT solutions, proving dimension reduction for 2 assets and developing a Sinkhorn algorithm.
result Dimension reduction to single-factor structure for 2-asset markets, significantly reducing computational time and improving accuracy.
Paper proposes conditional multidimensional scaling for better data reduction.
problem Mapping high-dimensional data to low-dimensional space with known features.
method Developed a broad class of methods called conditional multidimensional scaling (MDS) with an optimization algorithm.
result Conditional MDS improves estimation quality and simplifies visualization and knowledge discovery.
Proposes PredVAR model for reduced-dimensional dynamics from noisy data.
problem Extracting low-dimensional dynamics from high-dimensional noisy data.
method Probabilistic reduced-dimensional vector autoregressive model with oblique projection.
result Iterative algorithm yields dynamic latent variables with rank-ordered predictability.
New methods interpret clustering outcomes without altering data structure.
problem Post-processing methods destroy data integrity and obscure interpretations.
method Algorithm-agnostic interpretation methods using permutation feature importance, individual conditional expectation, and partial dependence.
result Preserves original feature structure and explains clustering outcomes.
New method for reducing dimensions of distributional data.
problem Nonlinear sufficient dimension reduction for distribution-on-distribution regression.
method Building universal kernels on metric spaces to characterize conditional independence.
result Method outperforms competing methods in synthetic and real data applications.
Develops a nonparametric graphical model for conditional independence.
problem Evaluation of conditional independence without distributional assumptions.
method Nonlinear sufficient dimension reduction techniques applied to a nonparametric graphical model.
result Method outperforms existing methods in non-Gaussian settings and high-dimensional data.
A new tensor-based layer reduces neural network dimensions without losing important features.
problem Reducing dimensionality in tensor-structured feature data for deep neural networks.
method TensorProjection layer that projects input tensors into output tensors with reduced dimensions through mode-wise projections.
result The TensorProjection layer outperforms traditional downsampling methods in tasks like medical image classification and segmentation.
Introduces top- regularization for better feature selection in machine learning.
problem Limited ability of existing feature selection methods to reconcile feature representativeness and inter-correlations.
method Top- regularization, which induces a sub-architecture on the model's architecture to select informative features and model complex relationships.
result Uniform approximation error bound for top- regularization approximating high-dimensional sparse functions.
Predicting the response of cancer cells to drugs is an important problem in pharmacogenomics. Recent efforts in generation of large scale datasets profiling gene expression and drug sensitivity in cell lines have provided a unique opportunity to study this problem. However, one major challenge is the small number of sa…
Dimensionality reduction techniques play an essential role in data analytics, signal processing and machine learning. Dimensionality reduction is usually performed in a preprocessing stage that is separate from subsequent data analysis, such as clustering or classification. Finding reduced-dimension representations tha…
Unified model for reducing dimensions and clustering high-dimensional data.
problem High-dimensional data clustering and dimensionality reduction.
method Hierarchical mixtures of Gaussians (HMoGs) with closed-form likelihood and inference.
result Efficiently models hundreds of latent dimensions, improving clustering performance.
This paper speeds up kernel methods using sparsified Gaussian sketches.
problem Kernel methods' computational limitations.
method Sparsified Gaussian sketches for kernel methods.
result Efficient time and space savings for kernel methods.
Contextual bandits with linear payoffs, which are also known as linear bandits, provide a powerful alternative for solving practical problems of sequential decisions, e.g., online advertisements. In the era of big data, contextual data usually tend to be high-dimensional, which leads to new challenges for traditional l…
Proposes MELODIC family for simultaneous binary logistic regression.
problem Simultaneous analysis of multiple binary response variables.
method Defines models in a reduced Euclidean space using a distance rule.
result Improves predictive accuracy through model interdependence.
The paper proposes differentially private sliced inverse regression algorithms for high-dimensional data.
problem Privacy concerns in high-dimensional data analysis.
method Differentially private sliced inverse regression algorithms designed for privacy preservation.
result Achieves minimax lower bounds up to logarithmic factors.
The sparse pseudo-input Gaussian process (SPGP) is a new approximation method for speeding up GP regression in the case of a large number of data points N. The approximation is controlled by the gradient optimization of a small set of M `pseudo-inputs', thereby reducing complexity from N^3 to NM^2. One limitation of th…
Bayesian surrogate models reduce uncertainty in high-dimensional design optimisation problems.
problem Uncertainty in high-dimensional inputs for complex computational models.
method Variational Bayesian inference for constructing statistical surrogates with Gaussian process priors and KL divergence for approximation.
result The RDVGP surrogate provides accurate and versatile approximations for robust structural optimisation.
Low-rank Characteristic Tensor Density Estimation Part II: Compression and Latent Density Estimationstat.ML
Paper proposes a novel auto-encoder for latent density estimation.
problem Challenges of learning generative probabilistic models due to curse of dimensionality.
method Joint dimensionality reduction and non-parametric density estimation framework using a novel estimator.
result Proposed model achieves promising results on various datasets.
New formulas for geodesics on Stiefel and flag manifolds using trust-region method.
problem Computing geodesics and logarithms on Stiefel and flag manifolds.
method Closed-form geodesic formulas, trust-region solver, Fréchet derivatives.
result Efficient computation of geodesic distance and logarithm map.
DPA preserves data distribution in reduced dimensions.
problem Loss of data distribution in dimension reduction.
method DPA combines encoder and decoder to match data distribution.
result DPA successfully reconstructs data distribution.
Acoustic Neighbor Embeddingseess.AS
Acoustic Neighbor Embeddings map speech and text to fixed dimensions for phonetic confusability.
problem Mapping speech and text to fixed dimensions for phonetic confusability.
method Adapting SNE to sequential inputs, training two encoder neural networks.
result More accurate results with low-dimensional embeddings in word recognition tasks.
Method infers causal structure from system behaviors using RKHS and kernel -machines.
problem Discovering causal structure in systems with varying external and measurement noise.
method Combines causal states and RKHS for efficient representation and inference of causal structure.
result Robustly estimates causal structure in high-dimensional data with varying noise.
Hybrid approach improves crude oil price forecasting using multi-scale data.
problem Forecasting crude oil prices with multi-scale data.
method Hybrid approach combining K-means, KPCA, and KELM.
result Hybrid approach outperforms traditional methods in both level and directional forecasting accuracy.
Computing optimal transport (OT) between measures in high dimensions is doomed by the curse of dimensionality. A popular approach to avoid this curse is to project input measures on lower-dimensional subspaces (1D lines in the case of sliced Wasserstein distances), solve the OT problem between these reduced measures, a…
TERA method speeds up derivative Gaussian processes in high dimensions.
problem High-dimensional function evaluations and gradient computations are computationally expensive.
method TERA uses exact gradient reduction to decouple and from the computational cost.
result TERA achieves state-of-the-art predictive accuracy with orders of magnitude faster computation.
This paper improves recommender systems by handling dynamic user preferences and item popularity.
problem Dynamic user preferences and changing item popularity in recommender systems.
method Developed a Thompson sampling-based policy for a high-dimensional linear bandit problem, reducing feature vector dimensionality and using exponentially increasing weights.
result Proved a regret bound that scales with the reduced dimension, demonstrating effectiveness in trade-off between computational complexity and regret performance.
New method uses neural networks to identify sources from limited data in complex systems.
problem Identifying sources from noisy and limited data in high-dimensional systems.
method Calibrating deep neural network surrogates to ensemble simulations and using Bayesian optimization for source identification.
result Reliable source identification with uncertainty quantification using limited data and auxiliary processes.
A method for reducing dimensions in Fréchet regression models.
problem Complex data objects in metric space-valued responses.
method Mapping metric-space valued random objects to real-valued variables and applying classical SDR.
result Consistent and asymptotically convergent method for Fréchet SDR.
New model selects uncorrelated and discriminative features for unsupervised feature selection.
problem Selecting uncorrelated and discriminative features in high-dimensional data.
method Adaptive graph-based generalized regression model with uncorrelated constraint and -norm regularization.
result The model effectively selects uncorrelated and discriminative features, improving clustering performance.
Combines datasets to improve model fitting with small sample sizes.
problem Improving model performance with limited samples from at least one dataset.
method Proposes a novel framework called Combine datasets based on Imputation (ComImp) and PCA-ComImp for combining datasets with missing data.
result Significant improvement in model accuracy, especially with small datasets and when combined with transfer learning.
Coarse-Graining Hamiltonian Systems Using WSINDyphysics.comp-ph
WSINDy identifies reduced Hamiltonian systems from particle interactions.
problem Coarse-graining Hamiltonian dynamics with approximate symmetries.
method WSINDy algorithm applied to Hamiltonian systems with timescale separation.
result WSINDy successfully identifies reduced Hamiltonian systems from noisy data.
Grassmannian diffusion maps based dimension reduction and classification for high-dimensional datacs.LG
GDMaps reduces high-dimensional data to lower dimensions for better classification.
problem High-dimensional data classification and representation.
method Grassmannian Diffusion Maps technique for nonlinear dimensionality reduction.
result GDMaps effectively identifies intrinsic subspace structures in high-dimensional data.
Reduced Order Modeling of Energetic Materials Using Physics-Aware Recurrent Convolutional Neural Networks in a Latent Space (LatentPARC)cond-mat.mtrl-sci
Reduced order modeling of energetic materials using physics-aware neural networks.
problem Simulating complex spatiotemporal dynamics in energetic materials.
method Physics-aware recurrent convolutions (PARC) combined with latent space projection to accelerate model training and inference.
result Significant decrease in training and inference time with comparable accuracy.