A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
New algorithm proves deep networks can learn better than shallow ones.
problem Understanding the power difference between shallow and deep neural networks.
method Identifying a class of Boolean functions and proving that logarithmic-depth networks can learn them efficiently using hierarchical reconstruction.
result First algorithmic separation between constant-depth and logarithmic-depth neural networks.
ANTs integrate neural networks and decision trees for better performance.
problem Combining neural networks and decision trees for improved performance.
method Adaptive Neural Trees (ANTs) integrate representation learning into decision tree structures, using backpropagation for adaptive growth.
result ANTs achieve competitive performance on classification and regression datasets, with benefits in lightweight inference, feature separation, and adaptable architecture.
Hierarchical clustering is a popular method for analyzing data which associates a tree to a dataset. Hartigan consistency has been used extensively as a framework to analyze such clustering algorithms from a statistical point of view. Still, as we show in the paper, a tree which is Hartigan consistent with a given dens…
MSOL learns hierarchical policies for multitask tasks with soft options.
problem Training hierarchical policies for multiple tasks with stability and flexibility.
method MSOL uses separate variational posteriors for each task, regularized by a shared prior, to avoid instabilities and fine-tune options for new tasks.
result MSOL significantly outperforms hierarchical and flat transfer-learning baselines.
In image classification, visual separability between different object categories is highly uneven, and some categories are more difficult to distinguish than others. Such difficult categories demand more dedicated classifiers. However, existing deep convolutional neural networks (CNN) are trained as flat N-way classifi…
Due to myriads of classes, designing accurate and efficient classifiers becomes very challenging for multi-class classification. Recent research has shown that class structure learning can greatly facilitate multi-class learning. In this paper, we propose a novel method to learn the class structure for multi-class clas…
We derive a statistical model for estimation of a dendrogram from single linkage hierarchical clustering (SLHC) that takes account of uncertainty through noise or corruption in the measurements of separation of data. Our focus is on just the estimation of the hierarchy of partitions afforded by the dendrogram, rather t…
We present memory-efficient and scalable algorithms for kernel methods used in machine learning. Using hierarchical matrix approximations for the kernel matrix the memory requirements, the number of floating point operations, and the execution time are drastically reduced compared to standard dense linear algebra routi…
Deep convolutional networks provide state of the art classifications and regressions results over many high-dimensional problems. We review their architecture, which scatters data with a cascade of linear filter weights and non-linearities. A mathematical framework is introduced to analyze their properties. Computation…
HPPCA improves imputation of longitudinal data with missing values.
problem Handling incomplete, high-dimensional longitudinal data with nested sources of variation and temporal dependency.
method Hierarchical probabilistic principal component analysis (HPPCA) with a two-level latent factor model and Gaussian process.
result HPPCA outperforms standard PPCA and multivariate functional PCA in imputation accuracy, even under heavy missingness and model misspecification.
An empirical analysis of interest rates in money and capital markets is performed. We investigate a set of 34 different weekly interest rate time series during a time period of 16 years between 1982 and 1997. Our study is focused on the collective behavior of the stochastic fluctuations of these time-series which is in…