The paper examines linking numbers in grid models and finds polynomial moments.
problem Analyzing linking numbers in grid models.
method Examined linking numbers as a random variable on isotopy classes of 2-component links, computed moments and limits.
result The uth moment of the linking number is a polynomial in the grid size with degree d≤u, and all odd moments vanish. A new approach models exploration in continuous-time RL using random measures.
problem Modeling exploration in continuous-time reinforcement learning.
method Random measure approach to control execution in continuous-time RL.
result Grid-sampling limit SDE can replace existing models for theoretical analysis and learning algorithms.
New model solves PDEs using probabilistic random grids.
problem Solving parametric PDEs with probabilistic collocation grids.
method Random Grid Neural Processes (RGNPs) with GICNets.
result Significant computational advantages and improved predictive capabilities.
The study models insurance dependence using Bernstein copulas.
problem Modeling dependence structures in nonlife insurance data.
method Review and suggest fitting Bernstein copulas to empirical data.
result Monte Carlo simulation and PML estimation for aggregate losses.
Study on typical knots and links using grid diagrams, focusing on size, components, and writhe.
problem Understanding the statistical behavior of knots and links, especially their typical properties.
method Modeling knots and links with grid diagrams, examining three invariants: size, components, and writhe, through numerical analysis.
result The size of a random knot is uniformly distributed and linearly dependent on grid size, while the number of components follows a distribution whose mean and variance grow with log_2 of grid size.
New high-order approximations for CIR process using random grids.
problem Approximating the Cox-Ingersoll-Ross process with high order.
method Combining discretization schemes on different random grids.
result Weak approximations of order 2k for all k∈N∗. We consider the symmetric exclusion process on suitable random grids that approximate a compact Riemannian manifold. We prove that a class of random walks on these random grids converge to Brownian motion on the manifold. We then consider the empirical density field of the symmetric exclusion process and prove that it …
Scalable algorithm for sampling Gaussian processes using sparse grids and preconditioners.
problem Generating high-dimensional Gaussian random vectors for GP sampling is computationally challenging.
method Proposes a scalable algorithm using inducing points approximation with sparse grids and additive Schwarz preconditioners.
result Demonstrates the efficacy and accuracy of the proposed method through experiments and comparisons.
A new Randomized-Hyperopt method improves XGBoost hyperparameter tuning.
problem Improving the performance of XGBoost through hyperparameter optimization.
method Proposes Randomized-Hyperopt for XGBoost hyperparameter tuning.
result Randomized-Hyperopt outperforms other methods in terms of accuracy and execution time.
Proposes a neural network for calibrating stochastic volatility models.
problem Calibrating stochastic volatility models with robustness and efficiency.
method Combines grid approach with pointwise two-stage calibration, using random grids for training.
result Validates the approach with empirical and Monte Carlo experiments for rough Bergomi and Heston models.
In this paper, we compare the three most popular algorithms for hyperparameter optimization (Grid Search, Random Search, and Genetic Algorithm) and attempt to use them for neural architecture search (NAS). We use these algorithms for building a convolutional neural network (search architecture). Experimental results on…
Inexact acquisition solutions in BO lead to sublinear cumulative regret.
problem Inexact maximization of acquisition functions in Bayesian optimization.
method Define inaccuracy measure, establish cumulative regret bounds for GP-UCB and GP-TS.
result Inexact BO algorithms can achieve sublinear cumulative regret under appropriate inaccuracy conditions.
Context: One of the black arts of data mining is learning the magic parameters which control the learners. In software analytics, at least for defect prediction, several methods, like grid search and differential evolution (DE), have been proposed to learn these parameters, which has been proved to be able to improve t…
Distribution grid is the medium and low voltage part of a large power system. Structurally, the majority of distribution networks operate radially, such that energized lines form a collection of trees, i.e. forest, with a substation being at the root of any tree. The operational topology/forest may change from time to …
In the monitoring of a complex electric grid, it is of paramount importance to provide operators with early warnings of anomalies detected on the network, along with a precise classification and diagnosis of the specific fault type. In this paper, we propose a novel multi-stage early warning system prototype for electr…
The paper develops a stationary-distribution theory for Random Forest ensemble size selection.
problem Determining the optimal number of trees in Random Forests.
method Modeling the ensemble size as a birth-death Markov chain and deriving its stationary distribution.
result The stationary ensemble size B∗ scales as O(ε−2) as ε↓0. Smart grid is an emerging and promising technology. It uses the power of information technologies to deliver intelligently the electrical power to customers, and it allows the integration of the green technology to meet the environmental requirements. Unfortunately, information technologies have its inherent vulnerabil…
PhI-GPR improves power grid state estimation and forecasting.
problem Accurate state estimation and forecasting in power grids with sparse measurements.
method Physics-informed Gaussian process regression (PhI-GPR) for stochastic differential equations.
result PhI-GPR provides more accurate forecasts and estimates of power grid states compared to ARIMA.
New sampling bounds improve uniform coverage verification in machine learning.
problem Conservative bounds in classical coverage analyses at small failure probabilities.
method Variance-based analysis of uniform random sampling on a d-dimensional unit hypercube. result Sample complexity bound with logarithmic dependence on failure probability.
SMAC method optimizes tree-boosting hyperparameters best.
problem Optimizing hyperparameters for tree-boosting to improve model accuracy.
method Compared and evaluated various hyperparameter optimization methods.
result SMAC method outperforms other methods for hyperparameter tuning.
While statistical learning methods have proved powerful tools for predictive modeling, the black-box nature of the models they produce can severely limit their interpretability and the ability to conduct formal inference. However, the natural structure of ensemble learners like bagged trees and random forests has been …
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.
We study random knots and links in R^3 using the Petaluma model, which is based on the petal projections developed by Adams et al. (2012). In this model we obtain a formula for the distribution of the linking number of a random two-component link. We also obtain formulas for the expectations and the higher moments of t…
Kernel method has been developed as one of the standard approaches for nonlinear learning, which however, does not scale to large data set due to its quadratic complexity in the number of samples. A number of kernel approximation methods have thus been proposed in the recent years, among which the random features metho…
LFGCN uses Levy Flights for graph semi-supervised learning.
problem Semi-supervised learning on graphs with improved performance.
method Lévy Flights into random walks, preferential P-DropEdge method.
result Significant improvement in classification performance, especially for heterogeneous graphs.
New insights into data geometry reveal manifold structure in grid-cell activity.
problem Understanding the roles of different dimensions in data geometry.
method Generalised Hanson-Wright inequality and random function model analysis.
result Persistence diagrams reveal latent homology and manifold structure.
We present a grid diagram analogue of Carter, Rieger and Saito's smooth movie theorem. Specifically, we give definitions for grid movies, grid movie isotopies and present a definition of grid planar isotopy as a particular subset of the grid diagram moves: stabilization, destabilization and commutation. We show that gr…
This paper introduces a generalization of Convolutional Neural Networks (CNNs) from low-dimensional grid data, such as images, to graph-structured data. We propose a novel spatial convolution utilizing a random walk to uncover the relations within the input, analogous to the way the standard convolution uses the spatia…
We designed a grid world task to study human planning and re-planning behavior in an unknown stochastic environment. In our grid world, participants were asked to travel from a random starting point to a random goal position while maximizing their reward. Because they were not familiar with the environment, they needed…
Model classifies hand gestures with low EMG samples augmented with noise.
problem Classify hand gestures with limited EMG data.
method Random variance Gaussian noise augmentation, Random Forest, XGBoost.
result High accuracy model for six hand gestures.
The paper introduces triple grid diagrams to construct Lagrangian surfaces in complex projective space.
problem Constructing Lagrangian surfaces in complex projective space.
method Defining and analyzing triple grid diagrams to determine Lagrangian caps and surfaces.
result Triple grid diagrams can determine closed Lagrangian surfaces in CP2 under certain conditions. This paper reviews hyperparameter optimization methods and best practices.
problem Finding optimal hyperparameters for machine learning models.
method Various hyperparameter optimization methods are reviewed, including grid search, random search, evolutionary algorithms, Bayesian optimization, Hyperband, and racing.
result Practical recommendations for conducting hyperparameter optimization are provided.
Bayesian optimization improves classifier selection for acute infection and mortality.
problem Improving accuracy of acute infection and mortality prediction.
method Comparison of hyperparameter optimization methods (grid search, random sampling, Bayesian optimization).
result Bayesian optimization outperforms grid search or random sampling for in-hospital mortality classifiers.
Half grid diagrams prove every link can be represented by a special type of grid diagram.
problem Representing links using grid diagrams and related invariants.
method Defining half grid diagrams and constructing canonical pairs, proving equivalence to Jones' construction, relating to classical link invariants.
result Established a new method to relate the oriented Thompson index to classical link invariants and provided bounds for knot invariants.
Grid homology confirms the Upsilon invariant in knot theory.
problem Verifying the equivalence of Upsilon invariants in knot theory.
method Reconstructed Upsilon invariant using grid homology and proved equivalence.
result Upsilon invariants in knot Floer and grid homology are equivalent.
GridPyM handles grid diagrams for knot theory.
problem Handling grid diagrams for knot theory.
method Generates and simplifies grids, models local transformations.
result Models local transformations between grid diagrams.
Grid homology theory for spatial graphs extends skein sequence.
problem No specific problem stated; focuses on extending a sequence.
method Defined grid homology theory for spatial graphs and extended skein sequence.
result Skein exact sequence extended to grid homology for spatial graphs.
Extends knot invariant to filtered grid complexes.
problem Knot invariants and grid complexes.
method Combining Ozsváth-Szabó-Stipsicz crossing-change maps with Alishahi-Eftekhary l(K) invariant.
result Combinatorial formulation of knot invariant.
New method finds grid diagrams for many fibered knots.
problem Detecting fibered knots using grid diagrams.
method Developed an efficient method to identify grid diagrams with unique maximal Alexander grading states.
result Found suitable grid diagrams for 5385 of 5397 fibered prime knots with crossing number ≤ 13.
Grid homology properties for MOY graphs studied.
problem Defining and studying properties of grid homology for MOY graphs.
method Defined grid homology from Harvey and O'Donnol's work. Studied properties using oriented skein relation, edge contraction, and parallel edge unification.
result Properties of grid homology for MOY graphs were studied and defined.
Grid homology invariant proved for lens space links.
problem Proving combinatorial invariance of grid homology for lens space links.
method Combining combinatorial methods with sign assignments to prove invariance.
result Grid homology is a link invariant for lens space links.
New trading strategy beats traditional grid in crypto markets.
problem Low expected return of traditional grid trading strategy.
method Dynamic Grid Trading (DGT) strategy that adapts to market conditions.
result DGT strategy outperforms traditional grid and buy-and-hold strategies.
New method constructs moduli spaces of Lagrangian surfaces in CP^2 from grid diagrams.
problem Constructing explicit examples of triple grid diagrams for Lagrangian surfaces in CP^2.
method Elegant geometric construction reducing to linear algebra.
result Explicit construction of moduli space of triple grid diagrams.
Develops equivariant grid homology for strongly invertible knots.
problem Invariants of strongly invertible knots.
method Equivariant grid diagrams and mapping cones.
result Equivariant unknotting numbers and genus bounds.
Grid homology shows knot unknotting lower bound.
problem Knot unknotting number determination
method Grid homology analysis
result Torsion homology classes order bounds unknotting number
Computes homology of an obstruction chain complex in grid homology.
problem Computing the homology of an obstruction chain complex in grid homology.
method Defined and computed the homology of the obstruction chain complex of the full grid.
result Results about the existence of sign assignments in grid homology.
SKI accelerates GP inference with sparse grids to handle higher dimensions.
problem SKI scales poorly in high dimensions due to dense grid size.
method Sparse grids within SKI framework, novel matrix-vector multiplication algorithm.
result SKI can be scaled to higher dimensions while maintaining accuracy.
We develop the idea of using Monte Carlo sampling of random portfolios to solve portfolio investment problems. In this first paper we explore the need for more general optimization tools, and consider the means by which constrained random portfolios may be generated. A practical scheme for the long-only fully-invested …