The paper examines the co-rank of weakly parafree 3-manifold groups and provides counterexamples.
problem Investigating the co-rank of weakly parafree 3-manifold groups and their relationship to free groups.
method Constructing specific examples of homology handlebodies and analyzing their fundamental groups.
result The fundamental group of W. Thurston's tripus manifold is not very large, showing that weakly parafree groups of rank at least 3 are not necessarily very large.
We present a parallelized bijective graph matching algorithm that leverages seeds and is designed to match very large graphs. Our algorithm combines spectral graph embedding with existing state-of-the-art seeded graph matching procedures. We justify our approach by proving that modestly correlated, large stochastic blo…
The paper proposes an efficient method to scale Bayesian inference for mixed multinomial logit models to very large datasets.
problem Efficiency in Bayesian inference for mixed multinomial logit models on large datasets.
method Amortized Variational Inference with stochastic backpropagation, automatic differentiation, and GPU acceleration.
result The proposed method achieves significant computational speedups over traditional methods for large datasets.
Deep GNNs and self-supervision boost graph learning at scale.
problem Efficiently deploying GNNs at large scale remains challenging.
method Two large-scale GNNs: a deep transductive node classifier and a very deep inductive graph regressor.
result Award-level performance on MAG240M and PCQM4M benchmarks.
Efficiently trains large corpora models without sampling.
problem Training neural network embedding models on very large corpora using SGD is expensive.
method Proposes new methods to train models without sampling unobserved pairs, using Gramian estimation and variance reduction schemes.
result Significant improvement in training time and generalization quality compared to traditional methods.
Stochastic EP improves memory efficiency for large datasets in Gaussian process classification.
problem Memory limitations in EP for large datasets.
method Stochastic Expectation Propagation (EP) for large scale Gaussian process classification.
result Stochastic EP avoids memory scaling with dataset size, improving scalability.
Large knots have very varied boundary slopes.
problem Understanding the variability of boundary slopes in knots.
method Analyzing alternating knots and their boundary slopes.
result The ratio of boundary slope diameter to crossing number can be arbitrarily large.
Study volatility models with rough paths, focusing on large deviations and option behavior.
problem Analyzing volatility in financial markets with very rough paths.
method Introduced time-inhomogeneous stochastic volatility models with Volterra Gaussian processes.
result Obtained large deviation principles for log-price processes in super rough Gaussian models.
New method clusters large datasets using geometric properties.
problem Clustering large datasets using DBSCAN* and HDBSCAN* is infeasible.
method Exploiting Euclidean space geometry, systematically construct clusters from subsets of data.
result Clusters of large datasets are possible with controlled subset sizes.
New LAMB optimizer reduces BERT training time from 3 days to 76 minutes.
problem Training large deep neural networks on massive datasets is computationally challenging.
method Developed a new layerwise adaptive large batch optimization technique called LAMB.
result LAMB reduces BERT training time from 3 days to 76 minutes using very large batch sizes.
DAC improves associative classification for very large datasets with high scalability and quality.
problem Handling large datasets with many categorical features.
method DAC uses ensemble learning, parallel processing, and pruning techniques.
result DAC outperforms state-of-the-art solutions in prediction quality and execution time.
New scalable methods for robust model learning from large datasets.
problem Training robust models resistant to data distribution shifts.
method Composite optimization for distributionally robust optimization (DRO).
result Scalable methods for learning robust models from large datasets.
ESCHER avoids importance sampling to estimate regret in large games.
problem Estimating Nash equilibria in large games with high variance.
method Computes a history value function to estimate regret without importance sampling.
result ESCHER reduces regret estimation variance significantly compared to existing methods.
Active learning improves CNN performance by selecting a subset of images.
problem Efficiently choosing images for training deep models on large datasets.
method Core-set selection approach for active learning.
result Proposed method significantly outperforms existing active learning approaches.
We consider the problem of simultaneously learning to linearly combine a very large number of kernels and learn a good predictor based on the learnt kernel. When the number of kernels d to be combined is very large, multiple kernel learning methods whose computational cost scales linearly in d are intractable. We p…
In this paper, we construct a family of asymptotically hyperbolic manifolds with horizons and with scalar curvature equal to -6. The manifolds we constructed can be arbitrary close to anti-de Sitter-Schwarzschild manifolds at infinity. Hence, the mass of our manifolds can be very large or very small. The main arguments…
BayesDLL offers a PyTorch library for Bayesian deep learning with large models.
problem Bayesian inference for large-scale deep networks.
method Variational inference, MC-dropout, stochastic-gradient MCMC, Laplace approximation.
result BayesDLL can handle Vision Transformers and pre-trained model weights as priors.
In this paper we first use the result in [12] to remove the assumption of the L2 boundedness of Weyl curvature in the gap theorem in [9] and then obtain a gap theorem for a class of conformally compact Einstein manifolds with very large renormalized volume. We also uses the blow-up method to derive curvature est…
LS-RPCA reduces dimensionality of large datasets better than random projections.
problem Reducing dimensionality of very large datasets for better classification performance.
method Developed LS-RPCA, an extension of RPCA for large datasets, to compare with random projections.
result LS-RPCA significantly improves classification performance over random projections.
A faster method for visualization recommendations on large datasets.
problem Infeasibility of state-of-the-art vis-rec models on large datasets due to high computational time.
method Reinforcement-learning (RL) framework that identifies optimal statistics within a time budget.
result Significantly reduces time-to-visualize with minimal error compared to baseline approaches.
Optimal student loan repayment strategies vary based on loan size.
problem Finding the most cost-effective repayment strategy for federal student loans.
method Analyzing the impact of different repayment strategies on total cost for varying loan sizes.
result Optimal repayment strategies depend on the loan balance, with different approaches for small, large, and intermediate balances.
Bayesian approach enhances SML for big data.
problem Feature discovery from large data sets.
method Bayesian decision theory applied to SML.
result Many SML techniques are connected to Bayesian inference.
Accurate approximations to density functionals have recently been obtained via machine learning (ML). By applying ML to a simple function of one variable without any random sampling, we extract the qualitative dependence of errors on hyperparameters. We find universal features of the behavior in extreme limits, includi…
Extends saddle-point method for large-time volatility smiles.
problem Analyzing large-time volatility smiles in financial models.
method Saddle-point approach to derive large-time model-implied volatility smiles.
result Provides theoretical foundation and wide class of arbitrage-free parametrizations.
This paper evaluates LLMs on large graph property estimation tasks.
problem Limited context length of LLMs limits their evaluation on large graphs.
method Developed EstGraph dataset and introduced four tasks for LLMs to estimate large graph properties.
result LLMs perform better on graph property estimation tasks when provided with context-rich prompts based on random walks.
Efficient methods for sparse random projections improve classification accuracy in very high-dimensional data.
problem Handling very high-dimensional sparse data efficiently.
method Non-iterative and iterative classification methods using sparse random projections and Jaccard kernel.
result Non-iterative methods yield larger, more accurate models than iterative methods.
New method reduces SBL complexity from cubic to linear, improving scalability.
problem Sparse Bayesian Learning's high computational complexity for large feature spaces.
method DQN-SBL, a diagonal Quasi-Newton method for SBL.
result DQN-SBL achieves competitive generalization with sparse models, scaling well to large-scale problems.
We show that the Gromov boundary of the free factor graph for the free group Fn with n>2 generators is the space of equivalence classes of minimal very small indecomposable projective Fn-trees without point stabilizer containing a free factor equipped with a quotient topology. Here two such trees are equivalent if the …
Performing signal processing tasks on compressive measurements of data has received great attention in recent years. In this paper, we extend previous work on compressive dictionary learning by showing that more general random projections may be used, including sparse ones. More precisely, we examine compressive K-mean…
New method for efficient graph learning on large graphs.
problem High memory complexity for graph learning on large, non-sparse graphs.
method Approximate large graphs as intersecting communities, using a new graph regularity lemma.
result Efficient graph learning algorithm with linear memory and time complexity.
We consider large-scale studies in which it is of interest to test a very large number of hypotheses, and then to estimate the effect sizes corresponding to the rejected hypotheses. For instance, this setting arises in the analysis of gene expression or DNA sequencing data. However, naive estimates of the effect sizes …
Algorithm recovers large causal tree from small samples.
problem Determining causal structure in large gene networks.
method Algorithm that recovers tree with high accuracy under mild conditions.
result High accuracy in recovering causal tree from small samples.
Database theory and database practice are typically the domain of computer scientists who adopt what may be termed an algorithmic perspective on their data. This perspective is very different than the more statistical perspective adopted by statisticians, scientific computers, machine learners, and other who work on wh…
A new algorithm MBMF improves recommendation accuracy and speed for sparse datasets.
problem Sparse and fluctuating predictions in recommender systems.
method MBMF uses magnitude constraints and Spherical coordinates to optimize faster than existing methods.
result MBMF outperforms existing algorithms in accuracy and speed on synthetic and real datasets.
Two new algorithms select matrix rows and columns to preserve distances.
problem Preserving distances in large matrix visualizations.
method Selects rows and columns to preserve distances.
result Preserves distances as closely as possible.
A scalable version of MADD improves big-data classification speed.
problem High computational complexity of MADD in big data.
method Selecting a representative set and using Random Fourier Features.
result Achieves similar performance to MADD but at a fraction of the computing time.
A new algorithm reduces graph complexity for better dense subgraph analysis.
problem Mining dense subgraphs in large graphs for better analysis.
method Multi-stage graph peeling algorithm (M-PA) with two-stage data screening.
result M-PA produces similar dense subgraphs to the previous PA but with reduced graph complexity.
New insights into neural network training show some interpolating methods can generalize well, while others fail catastrophically.
problem Understanding why neural networks trained to interpolate can still generalize well or fail catastrophically.
method Analyzing empirical risk minimization (ERM) over large hypotheses classes, focusing on interpolating methods.
result Some interpolating ERM-like methods for large hypotheses classes provide good statistical guarantees, while others fail catastrophically.
Stochastic Frank-Wolfe method solves large-scale Lasso problems efficiently.
problem Sparse model optimization for large-scale Lasso regression.
method Randomized Stochastic Frank-Wolfe algorithm with convergence guarantees.
result Algorithm outperforms state-of-the-art methods on large datasets.
In this era of large-scale data, distributed systems built on top of clusters of commodity hardware provide cheap and reliable storage and scalable processing of massive data. Here, we review recent work on developing and implementing randomized matrix algorithms in large-scale parallel and distributed environments. Ra…
This paper uses Bayesian ARD to automatically determine utility functions for discrete choice models.
problem Challenging and time-consuming task in identifying optimal utility function specifications.
method Bayesian framework and automatic relevance determination (ARD) for data-driven utility function specification.
result The proposed DCM-ARD model accurately recovers true utility function specifications and outperforms previous methods.
The paper proposes scalable methods for selecting prototypes from large dissimilarity datasets.
problem Selecting good prototypes from large dissimilarity datasets.
method Genetic algorithms, dissimilarity-based hashing, unsupervised and supervised criteria.
result The methods select good prototypes efficiently from large datasets.
The paper shows how to efficiently generate large Gaussian process samples with reliability guarantees.
problem Generating large-scale Gaussian process samples efficiently and with reliability.
method Demonstrates scaling data generation to large \(n\) while providing high probability guarantees.
result Efficiently generates large Gaussian process samples with reliability guarantees.
New algorithm clusters sparse, high-dimensional texts efficiently.
problem Clustering very short texts with high dimensions and sparsity.
method Linear algebra-based subspace clustering algorithm.
result Algorithm performs competitively on text categorization tasks.
LVM and LVMB manifolds are a large family of examples of non kähler manifolds. For instance, Hopf manifolds and Calabi-Eckmann manifolds can be seen as LVMB manifolds. The LVM manifolds have a very natural action of the real torus and the quotient of this action is a simple polytope. This quotient allows us to relate c…
LVM and LVMB manifolds are a large family of examples of non kahler manifolds. For instance, Hopf manifolds and Calabi-Eckmann manifolds can be seen as LVMB manifolds. The LVM manifolds have a very natural action of the real torus and the quotient of this action is a simple polytope. This quotient allows us to relate c…
Contact forms on 3-manifolds can have very large systolic ratios.
problem Understanding the systolic ratios of contact forms on 3-manifolds.
method Analyzing the systolic ratio of contact forms defined by co-orientable contact structures.
result Contact forms on any closed 3-manifold can have arbitrarily large systolic ratios.
Paper develops machine learning methods to identify thermal models for HPC clusters.
problem Accurate thermal modeling for high-power HPC systems with diverse workloads.
method Advanced system identification algorithm combined with machine learning for data selection.
result Very accurate thermal models generated for HPC systems (average error < 1°C).