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.
Covariance pooling is a feature pooling method with good classification accuracy. Because covariance features consist of second-order statistics, the scale of the feature elements are varied. Therefore, normalizing covariance features using a matrix square root affects the performance improvement. When pooling methods …
A framework isolates and learns approximately shared features for better domain adaptation.
problem Reducing performance degradation in unseen domains using machine learning models.
method Statistical framework distinguishing feature utilities based on correlation variance across domains. Learning approximately shared features from source tasks and fine-tuning on target tasks.
result Improved population risk compared to previous results on both source and target tasks, resolving the paradox of feature selection.
This paper concerns a method of selecting a subset of features for a sequential logit model. Tanaka and Nakagawa (2014) proposed a mixed integer quadratic optimization formulation for solving the problem based on a quadratic approximation of the logistic loss function. However, since there is a significant gap between …
Improves efficiency of random feature approximations for dot product kernels.
problem Efficiency of random feature approximations for dot product kernels.
method Generalization of existing random feature approximations using complex-valued random features, theoretical analysis of variances, data-driven optimization approach.
result Complex-valued random features can significantly reduce the variances of approximations.
We consider the problem of improving kernel approximation via randomized feature maps. These maps arise as Monte Carlo approximation to integral representations of kernel functions and scale up kernel methods for larger datasets. Based on an efficient numerical integration technique, we propose a unifying approach that…
Mutual Information (MI) is often used for feature selection when developing classifier models. Estimating the MI for a subset of features is often intractable. We demonstrate, that under the assumptions of conditional independence, MI between a subset of features can be expressed as the Conditional Mutual Information (…
We study the approximation properties of random ReLU features through their reproducing kernel Hilbert space (RKHS). We first prove a universality theorem for the RKHS induced by random features whose feature maps are of the form of nodes in neural networks. The universality result implies that the random ReLU features…
Random Fourier features is one of the most popular techniques for scaling up kernel methods, such as kernel ridge regression. However, despite impressive empirical results, the statistical properties of random Fourier features are still not well understood. In this paper we take steps toward filling this gap. Specifica…
Nonlinear kernels can be approximated using finite-dimensional feature maps for efficient risk minimization. Due to the inherent trade-off between the dimension of the (mapped) feature space and the approximation accuracy, the key problem is to identify promising (explicit) features leading to a satisfactory out-of-sam…
We propose semi-random features for nonlinear function approximation. The flexibility of semi-random feature lies between the fully adjustable units in deep learning and the random features used in kernel methods. For one hidden layer models with semi-random features, we prove with no unrealistic assumptions that the m…
Kernel methods are powerful learning methodologies that allow to perform non-linear data analysis. Despite their popularity, they suffer from poor scalability in big data scenarios. Various approximation methods, including random feature approximation, have been proposed to alleviate the problem. However, the statistic…
A novel model uses ODE-based random features to model nonlinear dynamical systems.
problem Modeling highly nonlinear dynamical systems with uncertainty quantification.
method Compositions of physics-informed random features derived from ODEs, combined with deep Gaussian processes and approximate Bayesian inference.
result The model effectively captures nonlinear behavior in real-world multivariate time series data and achieves comparable performance to other models on benchmark tasks.
Kernel approximation using randomized feature maps has recently gained a lot of interest. In this work, we identify that previous approaches for polynomial kernel approximation create maps that are rank deficient, and therefore do not utilize the capacity of the projected feature space effectively. To address this chal…
In this paper we discuss policy iteration methods for approximate solution of a finite-state discounted Markov decision problem, with a focus on feature-based aggregation methods and their connection with deep reinforcement learning schemes. We introduce features of the states of the original problem, and we formulate …
Classifiers label data as belonging to one of a set of groups based on input features. It is challenging to obtain accurate classification performance when the feature distributions in the different classes are complex, with nonlinear, overlapping and intersecting supports. This is particularly true when training data …
Kernel methods offer the flexibility to learn complex relationships in modern, large data sets while enjoying strong theoretical guarantees on quality. Unfortunately, these methods typically require cubic running time in the data set size, a prohibitive cost in the large-data setting. Random feature maps (RFMs) and the…
Devoted to multi-task learning and structured output learning, operator-valued kernels provide a flexible tool to build vector-valued functions in the context of Reproducing Kernel Hilbert Spaces. To scale up these methods, we extend the celebrated Random Fourier Feature methodology to get an approximation of operator-…
Kernel methods are powerful and flexible approach to solve many problems in machine learning. Due to the pairwise evaluations in kernel methods, the complexity of kernel computation grows as the data size increases; thus the applicability of kernel methods is limited for large scale datasets. Random Fourier Features (R…
The paper tackles fair classification with multiple sensitive features.
problem Existing fair classification methods often consider a single sensitive feature, but in practice, individuals are defined by multiple sensitive features.
method Characterizes Bayes-optimal fair classifiers for multiple sensitive features under various fairness measures, proposing in-processing and post-processing algorithms.
result Bayes-optimal fair classifiers for multiple sensitive features are instance-dependent thresholding rules that rely on a weighted sum of group membership probabilities.
Random feature method approximates operators with theoretical guarantees and reduced computation.
problem Approximating operators between infinite dimensional Banach spaces using machine learning.
method Random feature operator learning method with theoretical guarantees and error bounds.
result The random feature method can achieve similar or better test errors than kernel-based methods and neural networks with significantly reduced training times.
In this article we propose building general-purpose function approximators on top of Haar Scattering Networks. We advocate that this architecture enables a better comprehension of feature extraction, in addition to its implementation simplicity and low computational costs. We show its approximation and feature extracti…
Non-linear kernel methods can be approximated by fast linear ones using suitable explicit feature maps allowing their application to large scale problems. We investigate how convolution kernels for structured data are composed from base kernels and construct corresponding feature maps. On this basis we propose exact an…