NetSMF efficiently embeds large networks by sparse matrix factorization.
problem Learning latent representations for large-scale networks efficiently.
method NetSMF leverages spectral sparsification to efficiently sparsify and factorize a dense matrix.
result NetSMF achieves high efficiency and effectiveness on large-scale networks.
Sharp scaling factor τ stabilizes deep ResNets and improves convergence.
problem Ensuring stable training of deep ResNets with gradient descent.
method Scaling the parametric branch by τ = O ( 1 / L ) τ=O(1/\sqrt{L}) τ = O ( 1/ L ) to guarantee stable training. result Gradient descent finds global minima for properly over-parameterized ResNets.
We speed up factor analysis on large neuroimaging datasets.
problem Processing large multi-subject neuroimaging datasets efficiently.
method Optimized multi-subject factor analysis methods for parallel processing.
result Strong scaling up to 5.5x with 1024 nodes and 32,768 cores.
CMTRF improves recommendation accuracy by transforming rating scales.
problem Non-linear transformation of rating scales disrupts low-rank structure in rating matrices.
method CMTRF performs regression up to unknown monotonic transforms over user segments, coupled with matrix factorization.
result CMTRF outperforms other baselines in synthetic and real-world datasets.
Introduces BMF for efficient matrix factorization of large data.
problem Efficiently factorizing large scale matrices with limited memory.
method Uses block matrix approach and factorization at a block level.
result Demonstrates faster convergence on large matrices.
Study shows how non-uniform scaling affects persistence diagrams.
problem Stability of persistence diagrams under non-uniform scaling.
method Explicit bounds on bottleneck distance derived for Euclidean scaling.
result Explicit bounds on the stability of persistence diagrams under non-uniform scaling.
Unintended effects from scaling neural network outputs with adaptive learning rates.
problem Adaptive learning rate optimization's behavior is altered by output scaling, leading to misinterpretation.
method Presented a modified optimization algorithm to mitigate unintended effects.
result Adaptive learning rate's effectiveness is significantly impacted by output scaling, especially for small scaling factors.
Study reveals how correlation matrix eigenvalues change with time scale in U.S. stocks.
problem Understanding how correlation structure of securities changes with time scale.
method Aggregated one-minute returns of 533 U.S. stocks at different time scales, estimated correlation matrix, lead-lag factor model.
result Emergence of several dominant eigenvalues as time scale increases.
The scaling properties of the time series of asset prices and trading volumes of stock markets are analysed. It is shown that similarly to the asset prices, the trading volume data obey multi-scaling length-distribution of low-variability periods. In the case of asset prices, such scaling behaviour can be used for risk…
Scaling ResNets requires careful consideration of the layer depth and output scaling factors.
problem Avoiding vanishing or exploding gradients in deep ResNets as depth increases.
method Probabilistic analysis and continuous-time limit interpretation of ResNets.
result The optimal scaling factor is α L = 1 L α_L = \frac{1}{\sqrt{L}} α L = L 1 for standard i.i.d. initializations. DS-FACTO optimizes factorization machines for large-scale datasets.
problem High memory overheads of factorization machines on large datasets.
method Hybrid-parallel stochastic optimization algorithm DS-FACTO.
result DS-FACTO reduces memory requirements and scales to large datasets.
FaStR improves scalability for time-aware RS with varying coefficients.
problem Limited applicability of structured regression models to large-scale data with categorical effects and many interactions.
method Combines structured additive regression and factorization approaches in a neural network-based model implementation.
result FaStR scales better and performs competitively with other time-aware RS in prediction performance.
New method scales features for better clustering.
problem Irregular features disrupt classification.
method Spectral clustering with modified feature scales.
result Outperforms existing methods in experiments.
A new method for efficient causal structure learning at scale.
problem Causal structure learning is computationally challenging at scale.
method Relaxed sparsest-permutation formulation with support-level relaxation and masked zero-fill incomplete Cholesky factorization.
result The method enables scalable comparison of candidate orderings and matches the accuracy of slower baselines.
Improves Gaussian process factor models for multi-population recordings.
problem Cubic runtime scaling with trial length and group number limits application to large-scale recordings.
method Two approximate approaches: inducing variables and frequency domain.
result Achieved orders of magnitude speed-up with minimal statistical performance impact.
Proposes a new multi-scale architecture for generative flows to improve log-likelihood and sampling quality.
problem Challenges of high-dimensional latent space in flow models.
method Data-dependent dimension factorization based on likelihood contribution heuristic.
result Improvements in log-likelihood score and sampling quality on image benchmarks.
Unified framework for fast large-scale portfolio optimization.
problem Efficient portfolio optimization for large-scale financial data.
method Incorporates shrinkage and regularization techniques, addressing multiple objectives.
result AP-Trees and PCA-based factor models consistently outperform other approaches in out-of-sample portfolio performance.
Kernel clustering algorithm improved for large datasets using incomplete Cholesky factorization.
problem Large memory usage in kernel-based clustering for large-scale datasets.
method Approximate the kernel matrix using incomplete Cholesky factorization and apply linear k k k -means clustering. result The proposed method achieves similar performance to kernel k k k -means clustering but handles large-scale datasets efficiently. FSGD uses latent factors to scale SGD for high-dimensional learning.
problem Scalable optimization in high-dimensional machine learning.
method Factor-Augmented SGD (FSGD) that operates on streaming data.
result Established theoretical framework for latent factor estimation error in SGD.
New maps for large-scale geometry factorize into monotone and light.
problem Large-scale analogues of topological monotone and light maps.
method Introducing coarsely monotone and coarsely light maps, showing factorization system, and proving stability.
result Coarsely monotone maps are stable under pullbacks in the coarse category.
SOFAR learns large-scale association networks efficiently.
problem Efficiently understanding large-scale response-predictor association networks.
method Sparse Orthogonal Factor Regression (SOFAR) via sparse singular value decomposition with orthogonality constraints.
result SOFAR achieves statistical efficiency and scientific insights.
Paper combines scalable BMF algorithms for web-scale datasets.
problem High computational cost of Bayesian Matrix Factorization.
method Combines Posterior Propagation and asynchronous distributed implementation.
result Substantial improvements in scalability on web-scale datasets.
Efficient knockoffs for large-scale feature selection.
problem Large-scale feature selection problems.
method Gaussian model-X knockoffs with efficient methods for solving semidefinite programs.
result Efficient knockoffs can be generated with linear complexity in the dimension.
Efficient CVI for NGFA improves GFA inference for large-scale data.
problem Inference limitations in GFA models for large-scale data.
method Collapsed variational inference for nonparametric Bayesian GFA.
result CVI algorithm effectively approximates NGFA posterior in collapsed space.
KFT improves tensor forecasting by incorporating side information.
problem Tensor factorization weaknesses in latent factors.
method Kernel Fried Tensor (KFT) with variational inference.
result Superior performance over LightGBM and FFM.
ABCDEFG learns causal graphs from interventional data efficiently.
problem Learning causal graphs from interventional data is challenging.
method Amortized Bayesian Causal Discovery of Extended Factor Graphs (ABCDEFG)
result Estimates a posterior distribution that identifies the true causal graph up to an equivalence class.
Boolean matrix factorization and Boolean matrix completion from noisy observations are desirable unsupervised data-analysis methods due to their interpretability, but hard to perform due to their NP-hardness. We treat these problems as maximum a posteriori inference problems in a graphical model and present a message p…
The paper proposes a new SDF scaled by time-varying volatility from S&P 500 options.
problem Estimating the SDF from option prices and predicting the equity premium.
method Utilizes S&P 500 options data to recover a stable, non-monotonic SDF.
result The SDF exhibits a hump on the put side, which transitions into a W-shape with maturity.
Discrete version of Liouville's theorem for simplicial complexes.
problem Finding equivalent simplicial complexes under discrete conformal equivalence.
method Proving an analogous statement for simplicial complexes, considering combinatorial equivalence and scale factors associated with vertices.
result All discretely conformally equivalent simplicial complexes are combinatorially equivalent.
The paper shows how to reduce quantization errors in neural networks.
problem Reducing degradation caused by quantization in neural networks.
method Factorizing network weights to inversely scale output channels without changing function.
result Proper factorizations significantly decrease quantization errors.
The paper proves that certain FLRW spacetimes cannot be extended past the big bang.
problem The singularity structure of FLRW spacetimes without particle horizons at the C 0 C^0 C 0 -level. method Analyzing the singularity structure of FLRW spacetimes with constant spatial curvature.
result A geometric obstruction prevents continuous spacetime extensions for a wide range of scale factors in the case of K = − 1 K=-1 K = − 1 . Study uses CNNs to upscale wind speed data from 100 km to 3 km, improving subgrid-scale variability.
problem Recovering fine-scale wind speed information from coarse data.
method Convolutional neural networks (CNNs) with different input configurations (coarse wind speed, fine-scale topography, diurnal cycle) were tested.
result CNN models with coarse wind and fine topography inputs perform best in generalizing to unseen regions.
Wavelet-based fANOVA method improves factor analysis.
problem Efficiently analyzing functional data with multiple factors.
method Bayesian hierarchical model with spike-and-slab mixture and NIG conjugate setup, combined with Markov grove graphical model.
result Method outperforms existing wavelet-domain fANOVA methods in various settings.
Study shows typical scales for manifolds with lower Ricci bounds.
problem Understanding typical scales in manifolds with lower Ricci curvature bounds.
method Analysis of collapsing sequences of Riemannian manifolds with uniform lower Ricci curvature bounds.
result Rescaled manifolds subconverge to a product of a Euclidean and a compact space.
Bayesian Temporal Factorization predicts multidimensional time series with missing data.
problem Predicting large-scale, multidimensional spatiotemporal data with missing values.
method Integrates low-rank matrix/tensor factorization and VAR process into a probabilistic model.
result Superior performance on real-world spatiotemporal data sets compared to existing methods.
Proposes a scalable algorithm for large-scale probabilistic tensor analysis.
problem Leveraging time constraints to capture evolving tensor data.
method Introduces a new tensor data split strategy and an efficient algorithm for stochastic Alternating Direction Method of Multipliers.
result Demonstrates that P 2 ^2 2 T 2 ^2 2 F is a highly effective and efficiently scalable algorithm. New algorithms improve NMF for extracting patterns from time series data.
problem Extracting short-lived temporal motifs from high-dimensional time series data.
method Extended HALS and ANLS algorithms for CNMF model.
result Improved performance on large-scale data compared to multiplicative updates.
In addressing the question of the time scales characteristic for the market formation, we analyze high frequency tick-by-tick data from the NYSE and from the German market. By using returns on various time scales ranging from seconds or minutes up to two days, we compare magnitude of the largest eigenvalue of the corre…
This paper improves linear system solving by optimizing matrix diagonal scaling.
problem Improving the condition number of a matrix for faster iterative methods.
method Left or right diagonal rescaling of the matrix A, with new bounds and algorithms.
result Jacobi preconditioning reduces A's condition number to within a quadratic factor of the best possible scaling.
Sparse coding--that is, modelling data vectors as sparse linear combinations of basis elements--is widely used in machine learning, neuroscience, signal processing, and statistics. This paper focuses on the large-scale matrix factorization problem that consists of learning the basis set, adapting it to specific data. V…
We propose Macau, a powerful and flexible Bayesian factorization method for heterogeneous data. Our model can factorize any set of entities and relations that can be represented by a relational model, including tensors and also multiple relations for each entity. Macau can also incorporate side information, specificall…
A robust algorithm for non-negative matrix factorization (NMF) is presented in this paper with the purpose of dealing with large-scale data, where the separability assumption is satisfied. In particular, we modify the Linear Programming (LP) algorithm of [9] by introducing a reduced set of constraints for exact NMF. In…
New method infers causal factors from large-scale data without full graph reconstruction.
problem Inferring causal variables from large-scale systems without full causal graph reconstruction.
method Supervised learning on simulated data using a neural network and subsampled-ensemble inference.
result Efficiently identifies causal relationships in large-scale gene regulatory networks.
Hybrid approach for large-scale network synchronization using KF and PTP.
problem Synchronization of large-scale networks in 5G.
method Combines Kalman Filtering and PTP for pairwise synchronization, and Factor Graphs and Belief Propagation for end-to-end synchronization.
result Error in offset estimation remains below 5 ns in simulations.
We study the daily trading volume volatility of 17,197 stocks in the U.S. stock markets during the period 1989--2008 and analyze the time return intervals τ τ τ between volume volatilities above a given threshold q. For different thresholds q, the probability density function P_q(τ) scales with mean interval <τ> as P_q(τ…
Recovering low-rank and sparse matrices from incomplete or corrupted observations is an important problem in machine learning, statistics, bioinformatics, computer vision, as well as signal and image processing. In theory, this problem can be solved by the natural convex joint/mixed relaxations (i.e., l_{1}-norm and tr…
A new factor analysis method using ICA reduces portfolio concentration and diversifies excess kurtosis.
problem Standard factor analysis suffers from issues with pairwise correlations of asset returns.
method Identifies factors based on non-Gaussianity instead of variance, using ICA.
result Fat-tailed portfolios significantly reduce portfolio concentration and winner-takes-all problem.
The paper analyzes geometric densities and compression radii for knot types.
problem Optimizing geometric quantities associated with knot types.
method Develops a factorization framework for scale-covariant size functionals.
result Different minimizing sequences for density, compression, packing, and ropelength problems.