Conventional principal component analysis (PCA) finds a principal vector that maximizes the sum of second powers of principal components. We consider a generalized PCA that aims at maximizing the sum of an arbitrary convex function of principal components. We present a gradient ascent algorithm to solve the problem. Fo…
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48 results for “Principal Networks”
New algorithm learns principal subspace from random samples.
problem Learning principal subspace from small random submatrices.
method Stochastic gradient descent algorithm for neural networks.
result Algorithm can handle infinite rows and columns.
Neural network models of early sensory processing typically reduce the dimensionality of streaming input data. Such networks learn the principal subspace, in the sense of principal component analysis (PCA), by adjusting synaptic weights according to activity-dependent learning rules. When derived from a principled cost…
A new method reduces data movement in neural network training.
problem Large data movement during neural network training.
method Streaming batch principal component analysis for low-rank updates.
result Effective training of convolutional neural networks with low overhead.
The paper uses a novel framework to learn option prices by imitating principal investor behavior.
problem Challenges in modeling stock price changes and decision making in equity markets.
method Non-deterministic Markov decision process, Bayesian deep neural network, reinforcement learning.
result Optimal option prices learned through imitation of principal investor behavior.
GT-PCA improves PCA for image and time series data.
problem Lack of robustness to transformations in PCA.
method GT-PCA is a neural network that estimates components invariant to specific transformations.
result GT-PCA outperforms alternative methods in synthetic and real data experiments.
Deep Neural Networks for image classification have been found to be vulnerable to adversarial samples, which consist of sub-perceptual noise added to a benign image that can easily fool trained neural networks, posing a significant risk to their commercial deployment. In this work, we analyze adversarial samples throug…
Designing and modifying complex hull forms for optimal vessel performances have been a major challenge for naval architects. In the present study, Principal Component Analysis (PCA) is introduced to compress the geometric representation of a group of existing vessels, and the resulting principal scores are manipulated …
Develops a new tensor PCA method for analyzing multiple network data.
problem Analyzing multiple large networks for dimensionality reduction.
method Semi-Symmetric Tensor PCA (SS-TPCA) for principal components analysis.
result SS-TPCA achieves the same estimation accuracy as classical matrix PCA, with error proportional to the square root of the number of vertices.
Two novel clustering methods improve community detection in networks.
problem Community detection in networks using principal components.
method Principal Component Clustering (PCC) and Normalized Principal Component Clustering (NPCC).
result NPCC provides significant improvement over PCC and RSC methods.
A new GNN architecture called coVariance neural network (VNN) improves stability and transferability of covariance matrix analysis.
problem Stability and transferability issues in covariance matrix analysis.
method Developed coVariance neural network (VNN) that operates on sample covariance matrices.
result VNN is more stable and transferable than PCA-based approaches.
L-CNNs maintain gauge symmetry on non-Abelian lattice theories.
problem Applying convolutional neural networks to non-Abelian lattice gauge theories while preserving gauge symmetry.
method Developed a geometric formulation of L-CNNs that are equivariant under global symmetries and gauge transformations.
result Convolutional operations in L-CNNs are a specific case of gauge-equivariant neural networks on SU() principal bundles.
Interpretability has become an important issue in the machine learning field, along with the success of layered neural networks in various practical tasks. Since a trained layered neural network consists of a complex nonlinear relationship between large number of parameters, we failed to understand how they could achie…
We present a novel algorithm (Principal Sensitivity Analysis; PSA) to analyze the knowledge of the classifier obtained from supervised machine learning techniques. In particular, we define principal sensitivity map (PSM) as the direction on the input space to which the trained classifier is most sensitive, and use anal…
Study on dynamics of non-linear autoencoders learning principal components.
problem Technical difficulty in studying non-linear autoencoders due to non-trivial correlations.
method Derive asymptotically exact equations for SGD training of shallow, non-linear autoencoders.
result Autoencoders learn principal components sequentially and tie weights are ineffective.
This paper develops GPCA for probability distributions using Otto-Wasserstein geometry.
problem Analyzing modes of variation in datasets of probability measures.
method Geodesic Principal Component Analysis (GPCA) on Wasserstein space with neural networks.
result Identification of geodesic curves that capture modes of variation in probability distributions.
New method finds smaller networks with similar performance to large models in fewer epochs.
problem Training large neural networks is computationally expensive and energy-intensive.
method Use PCA to identify a basis of hidden layer activations and reduce network parameters.
result Principal Component Networks (PCNs) can train faster and use less energy than overparameterized models without accuracy loss.
We propose a new method for supervised learning, especially suited to wide data where the number of features is much greater than the number of observations. The method combines the lasso () sparsity penalty with a quadratic penalty that shrinks the coefficient vector toward the leading principal components of …
Study evaluates financial anomaly detection methods on Canadian stock market.
problem Detecting financial anomalies in the Canadian stock market.
method Topological data analysis (TDA), principal component analysis (PCA), and neural network-based approaches.
result Neural network-based methods achieve the strongest performance in detecting financial anomalies.
We consider principal component analysis (PCA) in decomposable Gaussian graphical models. We exploit the prior information in these models in order to distribute its computation. For this purpose, we reformulate the problem in the sparse inverse covariance (concentration) domain and solve the global eigenvalue problem …
A new algorithm identifies interpretable network representations via subgraph count statistics.
problem Interpreting network-valued data samples.
method Principal Component Analysis for Networks (PCAN) and its fast sampling-based version (sPCAN).
result The PCAN and sPCAN methods provide informative and discriminatory features for network samples.
KPCA improves OoD detection by separating InD and OoD data.
problem Insufficiency of PCA in detecting OoD data from InD data.
method Kernel PCA (KPCA) with task-specific kernels.
result KPCA achieves superior OoD detection performance.
We use a principal-agent model to analyze the structure of a book-driven dealer market when the dealer faces competition from a crossing network or dark pool. The agents are privately informed about their types (e.g. their portfolios), which is something that the dealer must take into account when engaging his counterp…
Sparse spectral decomposition identifies overlapping communities in networks.
problem Estimating overlapping community memberships in networks where nodes can belong to multiple communities.
method Sparse principal subspace estimation with iterative thresholding.
result The fixed point of the algorithm corresponds to correct node memberships under the stochastic block model.
Network analysis improves risk assessment for surety bonds.
problem Network effects in surety bonds increase risk assessment complexity.
method Modelled contractor network as directed graph, extended Friedkin-Johnsen model with stochastic process.
result Network effects increase average risk for surety organizations.
Anomaly Detection on Financial Time Series by Principal Component Analysis and Neural Networksq-fin.ST
Proposes a method to detect anomalies in financial time series using PCA and neural networks.
problem Anomalies in financial time series lead to miscalibrated risk models.
method Extract features using PCA, define anomaly score with neural network, calibrate cutoff value.
result The proposed PCA NN approach outperforms other anomaly detection methods.
Neural networks learn patterns in random data, improving downstream performance.
problem Understanding what deep networks learn with random labels.
method Analytical and empirical study of convolutional and fully connected networks pre-trained on random labels.
result Pre-trained networks on random labels transfer faster to real datasets, despite specialization effects.
Deep equilibrium models estimate latent variables from data.
problem Estimating latent variables from data.
method Generalized exponential family models, deep equilibrium networks.
result Deep equilibrium models solve MAP estimates for latent and transformation parameters.
Paper proposes SDDP for improving time series forecasting with high-dimensional predictors.
problem Improving time series forecasting with high-dimensional predictors.
method SDDP framework that incorporates target variable and lagged observations into factor extraction process.
result SDDP improves predictive accuracy in time series forecasting.
New method embeds correlation networks to reveal underlying time series patterns.
problem Analyzing correlation networks derived from time series data.
method Spectral embedding of noisy correlation networks, leveraging Fourier basis elements.
result Spectral embedding recovers true vertex-level latent representations under suitable assumptions.
Analyzes SGD dynamics in two-layer networks, bridging different regimes.
problem Understanding SGD dynamics in high-dimensional and mean-field settings.
method Rigorous analysis via deterministic low-dimensional description of sufficient statistics.
result Infinite-width dynamics remains close to a low-dimensional subspace.
Introduces generalized principal bundles and connections, linking them to standard gauge theories.
problem Generalized principal bundles and connections in field theories.
method Local coordinate transformation laws and horizontal lifts.
result Generalized principal connections are associated to Lie group fiber bundle connections.
This work analyzes when contrastive models are close to PCA or kernel methods.
problem Understanding when contrastive models are equivalent to kernel methods or PCA.
method Analyzing the training dynamics of two-layer contrastive models with non-linear activation.
result Wide contrastive models with cosine similarity based losses are close to PCA.
Survey of embedding methods for high-dimensional and network data.
problem Embedding high-dimensional and nonlinear data structures in a lower-dimensional space.
method Survey of various embedding methods including principal curves, multidimensional scaling, graph-based methods, and topological embeddings.
result Discussion of the pros and cons of algorithmic machine learning and statistical modeling approaches.
Introduces principal fairness for fair decision-making.
problem Discrimination among similarly affected individuals.
method Uses principal stratification from causal inference.
result Explicitly accounts for decision impacts, not just protected attributes.
Study of semi-principal bundles using group actions and wreath products.
problem Understanding bundles with fibers as free -spaces.
method Defining semi-principal bundles, bases, and frame bundles; using wreath products and functors.
result Semi-principal bundles can be retracted to principal bundles, preserving parallel transport.
The paper classifies and determines properties of specific hypersurfaces in complex hyperbolic quadrics.
problem Analyzing Hopf hypersurfaces with constant principal curvatures in complex hyperbolic quadrics.
method Classification and determination of principal curvatures for hypersurfaces with different numbers of distinct curvatures.
result Classification and determination of principal curvatures for Hopf hypersurfaces with up to four distinct values.
Study estimates heterogeneous principal causal effects with binary treatments and intermediate variables.
problem Estimating subgroup effects within strata defined by potential values of an intermediate variable.
method Proposes a framework for estimating and forming confidence intervals for heterogeneous principal causal effects under principal ignorability assumption. Develops several estimators with varying robustness properties.
result Established large-sample theory and analyzed bias contributions of each approach.
Study on discrete surfaces with constant principal curvature for nanocarbon applications.
problem Understanding discrete geometry properties of nanocarbon materials.
method Developed discrete surface theory on 3-ary oriented trees, defined discrete principal directions, constructed examples of discrete CPC surfaces.
result Construction of discrete constant principal curvature surfaces, including discrete CPC tori.
The paper introduces a method for detecting principal communities and embedding vertices.
problem Detecting and embedding vertices in graphs with community structure.
method Principal graph encoder embedding method that detects principal communities and produces vertex embeddings.
result The method successfully detects principal communities and produces accurate vertex embeddings.
We enumerate all the principal congruence link complements in , there by answering a question of W. Thurston. Related articles: "Technical Report: All Principal Congruence Link Groups" (arXiv:1902.04722), "All Known Principal Congruence Links" (arXiv:1902.04426).
A new method for sparse PCA using orthogonal rotations and soft-thresholding.
problem Sparse PCA with a new basis using orthogonal rotations.
method Initialize with leading principal components, apply orthogonal rotation, and soft-threshold the rotated components.
result The proposed method is more stable and explains more variance compared to alternatives.
This paper considers the problem of estimating the principal eigenvector of a covariance matrix from independent and identically distributed data samples in streaming settings. The streaming rate of data in many contemporary applications can be high enough that a single processor cannot finish an iteration of existing …
Bayesian SPCA method tackles orthogonality constraint with spike and slab prior.
problem Bayesian SPCA method for high-dimensional data with orthogonality constraint.
method Parameter-expanded coordinate ascent variational inference (PX-CAVI) with spike and slab prior.
result PX-CAVI algorithm outperforms existing SPCA approaches in performance.
A study on how a principal can incentivize an agent to make better decisions in a repeated game.
problem Optimizing a principal's utility in a misaligned principal-agent bandit game.
method Developed nearly optimal learning algorithms for the principal's regret in multi-armed and linear contextual settings.
result The principal can iteratively learn an incentive policy to maximize her total utility.
Localized Sparse Principal Component Analysis of Multivariate Time Series in Frequency Domainstat.ME
The paper introduces a method for interpretable principal component analysis of high-dimensional time series.
problem Inconsistent and difficult-to-interpret principal component estimates in high-dimensional regimes.
method Localized sparse principal component analysis of spectral density matrices in frequency domain.
result Efficient algorithm for sparse-localized estimates of principal subspaces.
The paper solves the Integration Problem for principal connections.
problem Describing discrete connections associated with a principal connection.
method Using the Lie or derivative functor to induce connections on the principal bundle.
result For flat principal connections, the Integration Problem has a unique solution among flat discrete connections.
Principal component regression (PCR) is a two-stage procedure that selects some principal components and then constructs a regression model regarding them as new explanatory variables. Note that the principal components are obtained from only explanatory variables and not considered with the response variable. To addre…