Tag: random
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Random Features for Operator-Valued Kernels: Bridging Kernel Methods and Neural Operators
Random Features for Operator-Valued Kernels: Bridging Kernel Methods and Neural Operators arXiv:2603.00971v1 Announce Type: new Abstract: In this work, we investigate the generalization properties of random feature methods. Our analysis extends prior results for Tikhonov regularization to a broad class of spectral regularization techniques and further generalizes the setting to operator-valued kernels. This unified framework…
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A Theory of Diversity for Random Matrices with Applications to In-Context Learning of Schr”odinger Equations
A Theory of Diversity for Random Matrices with Applications to In-Context Learning of Schr”odinger Equations arXiv:2601.12587v1 Announce Type: new Abstract: We address the following question: given a collection ${mathbf{A}^{(1)}, dots, mathbf{A}^{(N)}}$ of independent $d times d$ random matrices drawn from a common distribution $mathbb{P}$, what is the probability that the centralizer of ${mathbf{A}^{(1)}, dots, mathbf{A}^{(N)}}$…
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Constructive Approximation of Random Process via Stochastic Interpolation Neural Network Operators
Constructive Approximation of Random Process via Stochastic Interpolation Neural Network Operators arXiv:2512.24106v1 Announce Type: new Abstract: In this paper, we construct a class of stochastic interpolation neural network operators (SINNOs) with random coefficients activated by sigmoidal functions. We establish their boundedness, interpolation accuracy, and approximation capabilities in the mean square sense, in probability, as well…
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Supervised Learning of Random Neural Architectures Structured by Latent Random Fields on Compact Boundaryless Multiply-Connected Manifolds
Supervised Learning of Random Neural Architectures Structured by Latent Random Fields on Compact Boundaryless Multiply-Connected Manifolds arXiv:2512.10407v1 Announce Type: new Abstract: This paper introduces a new probabilistic framework for supervised learning in neural systems. It is designed to model complex, uncertain systems whose random outputs are strongly non-Gaussian given deterministic inputs. The architecture itself is…
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Colored Markov Random Fields for Probabilistic Topological Modeling
Colored Markov Random Fields for Probabilistic Topological Modeling arXiv:2512.03727v1 Announce Type: new Abstract: Probabilistic Graphical Models (PGMs) encode conditional dependencies among random variables using a graph -nodes for variables, links for dependencies- and factorize the joint distribution into lower-dimensional components. This makes PGMs well-suited for analyzing complex systems and supporting decision-making. Recent advances in topological…
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An RKHS Perspective on Tree Ensembles
An RKHS Perspective on Tree Ensembles arXiv:2512.00397v1 Announce Type: new Abstract: Random Forests and Gradient Boosting are among the most effective algorithms for supervised learning on tabular data. Both belong to the class of tree-based ensemble methods, where predictions are obtained by aggregating many randomized regression trees. In this paper, we develop a theoretical framework…
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Empirical Likelihood for Random Forests and Ensembles
Empirical Likelihood for Random Forests and Ensembles arXiv:2511.13934v1 Announce Type: new Abstract: We develop an empirical likelihood (EL) framework for random forests and related ensemble methods, providing a likelihood-based approach to quantify their statistical uncertainty. Exploiting the incomplete $U$-statistic structure inherent in ensemble predictions, we construct an EL statistic that is asymptotically chi-squared when subsampling…
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What a Drunk Man Can Teach Us About Time Series Forecasting
What a Drunk Man Can Teach Us About Time Series Forecasting Autocorrelation & The Random Walk explained with a drunk man 🍺 Let me illustrate this statistical concept with an example we can all visualize. Imagine a drunk man wandering a city. His steps are completely random and unpredictable. Here’s the intuition: – His current…
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Asymptotic Study of In-context Learning with Random Transformers through Equivalent Models
Asymptotic Study of In-context Learning with Random Transformers through Equivalent Models arXiv:2509.15152v1 Announce Type: new Abstract: We study the in-context learning (ICL) capabilities of pretrained Transformers in the setting of nonlinear regression. Specifically, we focus on a random Transformer with a nonlinear MLP head where the first layer is randomly initialized and fixed while the…
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A Visual Guide to Tuning Random Forest Hyperparameters
A Visual Guide to Tuning Random Forest Hyperparameters How hyperparameter tuning visually changes random forests The post A Visual Guide to Tuning Random Forest Hyperparameters appeared first on Towards Data Science. James Gibbins Go to original source
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Learning graphons from data: Random walks, transfer operators, and spectral clustering
Learning graphons from data: Random walks, transfer operators, and spectral clustering arXiv:2507.18147v1 Announce Type: new Abstract: Many signals evolve in time as a stochastic process, randomly switching between states over discretely sampled time points. Here we make an explicit link between the underlying stochastic process of a signal that can take on a bounded continuum…
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A generative modeling / Physics-Informed Neural Network approach to random differential equations
A generative modeling / Physics-Informed Neural Network approach to random differential equations arXiv:2507.01687v1 Announce Type: new Abstract: The integration of Scientific Machine Learning (SciML) techniques with uncertainty quantification (UQ) represents a rapidly evolving frontier in computational science. This work advances Physics-Informed Neural Networks (PINNs) by incorporating probabilistic frameworks to effectively model uncertainty in complex systems.…
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Random feature approximation for general spectral methods
Random feature approximation for general spectral methods arXiv:2506.16283v1 Announce Type: new Abstract: Random feature approximation is arguably one of the most widely used techniques for kernel methods in large-scale learning algorithms. In this work, we analyze the generalization properties of random feature methods, extending previous results for Tikhonov regularization to a broad class of spectral…
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Asymptotic Normality of Infinite Centered Random Forests -Application to Imbalanced Classification
Asymptotic Normality of Infinite Centered Random Forests -Application to Imbalanced Classification arXiv:2506.08548v1 Announce Type: new Abstract: Many classification tasks involve imbalanced data, in which a class is largely underrepresented. Several techniques consists in creating a rebalanced dataset on which a classifier is trained. In this paper, we study theoretically such a procedure, when the classifier…
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A Kernelised Stein Discrepancy for Assessing the Fit of Inhomogeneous Random Graph Models
A Kernelised Stein Discrepancy for Assessing the Fit of Inhomogeneous Random Graph Models arXiv:2505.21580v1 Announce Type: new Abstract: Complex data are often represented as a graph, which in turn can often be viewed as a realisation of a random graph, such as of an inhomogeneous random graph model (IRG). For general fast goodness-of-fit tests in…
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Supervised Models Can Generalize Also When Trained on Random Label
Supervised Models Can Generalize Also When Trained on Random Label arXiv:2505.11006v1 Announce Type: new Abstract: The success of unsupervised learning raises the question of whether also supervised models can be trained without using the information in the output $y$. In this paper, we demonstrate that this is indeed possible. The key step is to formulate…
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How to Set the Number of Trees in Random Forest
How to Set the Number of Trees in Random Forest Scientific publication T. M. Lange, M. GĂĽltas, A. O. Schmitt & F. Heinrich (2025). optRF: Optimising random forest stability by determining the optimal number of trees. BMC bioinformatics, 26(1), 95. Follow this LINK to the original publication. Random Forest — A Powerful Tool for Anyone…
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Understanding Random Forest using Python (scikit-learn)
Understanding Random Forest using Python (scikit-learn) Decision trees are a popular supervised learning algorithm with benefits that include being able to be used for both regression and classification as well as being easy to interpret. However, decision trees aren’t the most performant algorithm and are prone to overfitting due to small variations in the training…
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High-dimensional ridge regression with random features for non-identically distributed data with a variance profile
High-dimensional ridge regression with random features for non-identically distributed data with a variance profile arXiv:2504.03035v1 Announce Type: new Abstract: The behavior of the random feature model in the high-dimensional regression framework has become a popular issue of interest in the machine learning literature}. This model is generally considered for feature vectors $x_i = Sigma^{1/2} x_i’$,…
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Nonlinear Principal Component Analysis with Random Bernoulli Features for Process Monitoring
Nonlinear Principal Component Analysis with Random Bernoulli Features for Process Monitoring arXiv:2503.12456v1 Announce Type: new Abstract: The process generates substantial amounts of data with highly complex structures, leading to the development of numerous nonlinear statistical methods. However, most of these methods rely on computations involving large-scale dense kernel matrices. This dependence poses significant challenges in…
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Bags of Projected Nearest Neighbours: Competitors to Random Forests?
Bags of Projected Nearest Neighbours: Competitors to Random Forests? arXiv:2503.09651v1 Announce Type: cross Abstract: In this paper we introduce a simple and intuitive adaptive k nearest neighbours classifier, and explore its utility within the context of bootstrap aggregating (“bagging”). The approach is based on finding discriminant subspaces which are computationally efficient to compute, and are…
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On Statistical Estimation of Edge-Reinforced Random Walks
On Statistical Estimation of Edge-Reinforced Random Walks arXiv:2503.06115v1 Announce Type: new Abstract: Reinforced random walks (RRWs), including vertex-reinforced random walks (VRRWs) and edge-reinforced random walks (ERRWs), model random walks where the transition probabilities evolve based on prior visitation history~cite{mgr, fmk, tarres, volkov}. These models have found applications in various areas, such as network representation learning~cite{xzzs},…
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Random Feature Representation Boosting
Random Feature Representation Boosting arXiv:2501.18283v1 Announce Type: new Abstract: We introduce Random Feature Representation Boosting (RFRBoost), a novel method for constructing deep residual random feature neural networks (RFNNs) using boosting theory. RFRBoost uses random features at each layer to learn the functional gradient of the network representation, enhancing performance while preserving the convex optimization benefits…
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Random Sparse Lifts: Construction, Analysis and Convergence of finite sparse networks
Random Sparse Lifts: Construction, Analysis and Convergence of finite sparse networks arXiv:2501.05930v1 Announce Type: cross Abstract: We present a framework to define a large class of neural networks for which, by construction, training by gradient flow provably reaches arbitrarily low loss when the number of parameters grows. Distinct from the fixed-space global optimality of non-convex…
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Robust random graph matching in dense graphs via vector approximate message passing
Robust random graph matching in dense graphs via vector approximate message passing arXiv:2412.16457v1 Announce Type: new Abstract: In this paper, we focus on the matching recovery problem between a pair of correlated Gaussian Wigner matrices with a latent vertex correspondence. We are particularly interested in a robust version of this problem such that our observation…