Study on random representations of surface groups into SU(n), focusing on asymptotic expansions.
problem Understanding random representations of surface groups into special unitary groups.
method Use of a symplectic form on moduli space, establishing asymptotic expansions for trace values.
result Existence of large n asymptotic expansions for expected values of trace of elements under random representations.
We systematically investigate the problem of representing Markov chains by families of random maps, and which regularity of these maps can be achieved depending on the properties of the probability measures. Our key idea is to use techniques from optimal transport to select optimal such maps. Optimal transport theory a…
Uniformly random permutations converge to regular representation on surface groups.
problem Understanding the behavior of random homomorphisms to symmetric groups.
method Polynomial approximation and random walk analysis.
result Strong convergence of random representations to regular representation.
Manifold learning seeks a low dimensional representation that faithfully captures the essence of data. Current methods can successfully learn such representations, but do not provide a meaningful set of operations that are associated with the representation. Working towards operational representation learning, we endow…
Dictionaries are collections of vectors used for representations of random vectors in Euclidean spaces. Recent research on optimal dictionaries is focused on constructing dictionaries that offer sparse representations, i.e., ℓ0-optimal representations. Here we consider the problem of finding optimal dictionaries …
UniNet efficiently learns network representations from large graphs.
problem Efficiently learning network representations from large graphs.
method Metropolis-Hastings sampling for efficient edge sampling and random walk model abstraction.
result UniNet outperforms existing NRL models on billion-edge networks.
New method uses random convex polytopes to measure representation quality.
problem Measuring the quality of deep learning representations.
method Random Polytope Descriptor method based on random convex polytopes.
result Regularization in autoencoders can degrade out-of-distribution detection.
RST improves environmental time series classification accuracy using randomized B-spline trees.
problem Improving accuracy in classifying complex environmental time series.
method Randomized Spline Trees (RST) integrates randomized functional representations into ensemble learning.
result RST variants outperform standard Random Forests and Gradient Boosting on most environmental time series datasets.
RFRBoost uses random features to boost deep residual neural networks, improving performance and computational efficiency.
problem Improving performance of deep residual neural networks (RFNNs) while preserving convex optimization benefits.
method Random Feature Representation Boosting (RFRBoost) using boosting theory and random features at each layer.
result RFRBoost significantly outperforms RFNNs and end-to-end trained MLP ResNets in small- to medium-scale tabular datasets.
This paper shows that deep learning (DL) representations of data produced by generative adversarial nets (GANs) are random vectors which fall within the class of so-called \textit{concentrated} random vectors. Further exploiting the fact that Gram matrices, of the type G=XTX with $X=[x_1,\ldots,x_n]\in \mathbb{R}…
Landmark-based node embeddings approximate shortest path distances in random graphs.
problem Capturing global graph distances in node representations.
method Landmark-based node embeddings using shortest path distances from a subset of reference nodes (landmarks).
result Random graphs require lower dimensions in landmark-based embeddings compared to worst-case graphs.
We introduce a training method for both better word representation and performance, which we call GROVER (Gradual Rumination On the Vector with maskERs). The method is to gradually and iteratively add random noises to word embeddings while training a model. GROVER first starts from conventional training process, and th…
Batch normalization makes deep neural networks' representations increasingly orthogonal.
problem Orthogonality of deep neural network representations.
method Random linear transformations in successive batch-normalizations.
result Orthogonality of representations improves SGD performance.
Random representations of surface groups approach asymptotic freeness in large n limit.
problem Asymptotic freeness of Haar unitary matrices for surface groups.
method Interplay between Dehn's work and classical invariant theory.
result Expected value of trace of a fixed non-identity element is bounded as no∞. Random matrix theory predicts neural representations generalize well.
problem Understanding why neural representations generalize well in practice.
method Applied random matrix theory to kernel regression and neural networks.
result GCV estimator accurately predicts generalization risk in overparameterized settings.
NodeSig efficiently computes binary node embeddings for scalable graph analysis.
problem Scalability issues in graph representation learning models.
method NodeSig uses random walk diffusion probabilities and stable random projections to compute binary node embeddings efficiently.
result NodeSig achieves a good balance between accuracy and efficiency on node classification and link prediction tasks.
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 a very high-dimensional vector space, two randomly-chosen vectors are almost orthogonal with high probability. Starting from this observation, we develop a statistical factor model, the random factor model, in which factors are chosen at random based on the random projection method. Randomness of factors has the con…
Study optimal hedging for claims with random weights in discrete time.
problem Optimal hedging for claims with random weights in discrete time.
method Explicit recursive representation of optimal hedging strategy, without ND condition.
result Obtained explicit optimal hedging strategy in a recursive form.
Representations based on random walks can exploit discrete data distributions for clustering and classification. We extend such representations from discrete to continuous distributions. Transition probabilities are now calculated using a diffusion equation with a diffusion coefficient that inversely depends on the dat…
We provide a dual representation of quasiconvex maps between two lattices of random variables in terms of conditional expectations. This generalizes the dual representation of quasiconvex real valued functions and the dual representation of conditional convex maps.
GraphMoE generates random graphs using neural networks and graphlets.
problem Learning generative models for random graphs.
method GraphMoE uses a neural network trained with graphlets and subgraph counts to match the distribution of random graphs.
result GraphMoE can generate graphs that mimic various real-world datasets and fool graph classifiers.
RR-GCN uses random transformations instead of learned weights for node embeddings.
problem Learning node embeddings in KGs.
method Random Relational Graph Convolutional Network (RR-GCN) with untrained parameters.
result RR-GCN can compete with fully trained R-GCNs in node classification and link prediction.
A new method uses SPDEs to efficiently model random fields on complex domains.
problem Efficient representation of random fields on complex domains for engineering and machine learning.
method Uses SPDEs to develop a scalable framework for statFEM and GP regression.
result Can model anisotropic, non-stationary random fields with arbitrary smoothness.
Random Forest proximity measures for multi-view classification.
problem Combining multiple heterogeneous data views for classification.
method Building dissimilarity representations for each view, fusing them dynamically.
result Dynamic View Selection improves multi-view classification performance.
Learning expressive low-dimensional representations of ultrahigh-dimensional data, e.g., data with thousands/millions of features, has been a major way to enable learning methods to address the curse of dimensionality. However, existing unsupervised representation learning methods mainly focus on preserving the data re…
Combines observational and randomized data to estimate treatment effects.
problem Estimating heterogeneous treatment effects using only observational data is biased.
method Two-step framework: learn shared structure from observational data, then data-specific structures from randomized data.
result Combining observational and randomized data improves treatment effect estimation.
An important part of many machine learning workflows on graphs is vertex representation learning, i.e., learning a low-dimensional vector representation for each vertex in the graph. Recently, several powerful techniques for unsupervised representation learning have been demonstrated to give the state-of-the-art perfor…
New framework to test neural network representation similarity measures.
problem Disagreements among dissimilarity measures in neural networks.
method Statistical testing framework to evaluate measures based on functional behavior.
result Current metrics have different weaknesses; a classical baseline performs surprisingly well.
We analyze generalization in deep learning models using random matrix theory.
problem Understanding the generalization error in deep learning models with random feature representations.
method Applying Random Matrix Theory to derive asymptotic generalization error formulas for various architectures.
result Linear ESNs are equivalent to ridge regression with exponentially time-weighted input covariance, revealing an inductive bias towards recent inputs.
We consider a market model where there are two levels of information. The public information generated by the financial assets, and a larger flow of information that contains additional knowledge about a random time. This random time can represent many economic and financial settings, such as the default time of a firm…
A new method for causal inference in high-dimensional data using machine learning.
problem Causal inference in high-dimensional observational data.
method Support Points Sample Splitting (SPSS) for efficient double machine learning (DML) in causal inference.
result Deep learning with SPSS and hybrid methods outperform SVM with SPSS in computational efficiency and estimation quality.
The paper describes how martingales can be represented after a random time in financial models.
problem Representing martingales after a random event in financial markets.
method Explicit representation of G-local martingales in terms of F-local martingales and parameters of the random time.
result Comprehensive representation of G-local martingales, complementing previous work.
Random projections help in representing sparse graphs efficiently.
problem Efficiently representing sparse graphs of varying sizes and vertex sets.
method Random projection of adjacency matrices to retain graph functionality and properties.
result Random projections can accurately represent graphs of different sizes and vertex sets in the same space.
Study shows label noise impacts neural representations' information content, revealing double descent behavior.
problem Impact of label noise on neural network hidden representations.
method Information Imbalance proxy of conditional mutual information to compare hidden representations.
result Representations learned with noisy labels are more informative than those with clean labels in the underparameterized regime, and equally informative in the overparameterized regime.
New RF dissimilarity measures improve multi-view learning accuracy.
problem Improving multi-view learning accuracy in HDLSS problems.
method Modified Random Forest proximity measures for HDLSS multi-view classification.
result Second method significantly more accurate than other state-of-the-art methods.
In this paper, we obtain stability results for martingale representations in a very general framework. More specifically, we consider a sequence of martingales each adapted to its own filtration, and a sequence of random variables measurable with respect to those filtrations. We assume that the terminal values of the m…
Random walks on braid groups are transient, with specific closure properties for certain braids.
problem Understanding the behavior of random walks on braid groups and their closure properties.
method Analyzing the symplectic representation of braid groups and polynomial conditions on their matrices.
result Random walks on braid groups are transient, and specific closure properties for certain braids are derived.
Dictionaries are collections of vectors used for representations of elements in Euclidean spaces. While recent research on optimal dictionaries is focussed on providing sparse (i.e., ℓ0-optimal,) representations, here we consider the problem of finding optimal dictionaries such that representations of samples of …
New method learns robust representations by modeling environment variation.
problem Learning invariant representations across varying environments.
method Explicitly modeling variation across environments and marginalizing it out.
result Proposed method outperforms invariant-learning methods in various settings.
Graph representation learning aims at transforming graph data into meaningful low-dimensional vectors to facilitate the employment of machine learning and data mining algorithms designed for general data. Most current graph representation learning approaches are transductive, which means that they require all the nodes…
Bayesian nonparametric approach for clustering non-exchangeable groups.
problem Clustering grouped data with dependencies among groups.
method Graphical Dirichlet process modeling with Markov property.
result Efficient posterior inference algorithm developed.
We establish general versions of a variety of results for quasiconvex, lower-semicontinuous, and law-invariant functionals. Our results extend well-known results from the literature to a large class of spaces of random variables. We sometimes obtain sharper versions, even for the well-studied case of bounded random var…
The random subspace method, known as the pillar of random forests, is good at making precise and robust predictions. However, there is not a straightforward way yet to combine it with deep learning. In this paper, we therefore propose Neural Random Subspace (NRS), a novel deep learning based random subspace method. In …
Neural networks learn spectral representations for group composition.
problem Understanding structured emergence in neural network training.
method Lifting gradient flow to Fourier domain, proving convergence to irreducible representations.
result Neurons converge to single irreducible representations, cross-layer coefficients align.
NURD improves model performance by distilling representations independent of nuisance variables.
problem Models trained under spurious correlations may fail on data with different nuisance-label relationships.
method Developed Nuisance-Randomized Distillation (NURD) to find representations independent of nuisance variables.
result NURD finds representations that perform better regardless of nuisance-label relationships.
We describe a method to perform functional operations on probability distributions of random variables. The method uses reproducing kernel Hilbert space representations of probability distributions, and it is applicable to all operations which can be applied to points drawn from the respective distributions. We refer t…
Graph-based state representation improves deep RL performance.
problem High sample-complexity and starting with a good input representation in deep RL.
method Exploiting the graph structure of MDPs for effective state representation learning.
result Graph-based node representation methods outperform matrix-based methods in grid-world navigation tasks.