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.
Band-limited SAC improves learning efficiency and stability in simulated environments.
Graph neural networks can be adapted to new graphs with a limit object called graphon NNs.
We study the problem of sampling k-bandlimited signals on graphs. We propose two sampling strategies that consist in selecting a small subset of nodes at random. The first strategy is non-adaptive, i.e., independent of the graph structure, and its performance depends on a parameter called the graph coherence. On the co…
In this work, we introduce the concept of bandlimiting into the theory of machine learning because all physical processes are bandlimited by nature, including real-world machine learning tasks. After the bandlimiting constraint is taken into account, our theoretical analysis has shown that all practical machine learnin…
GNNs outperform NNs in interpolating bandlimited functions on Euclidean cubes.
Bandlimited random neural networks may not approximate all functions perfectly.
Spectral clustering has become a popular technique due to its high performance in many contexts. It comprises three main steps: create a similarity graph between N objects to cluster, compute the first k eigenvectors of its Laplacian matrix to define a feature vector for each object, and run k-means on these features t…
We present a new random sampling strategy for k-bandlimited signals defined on graphs, based on determinantal point processes (DPP). For small graphs, ie, in cases where the spectrum of the graph is accessible, we exhibit a DPP sampling scheme that enables perfect recovery of bandlimited signals. For large graphs, ie, …
We study signal recovery on graphs based on two sampling strategies: random sampling and experimentally designed sampling. We propose a new class of smooth graph signals, called approximately bandlimited, which generalizes the bandlimited class and is similar to the globally smooth class. We then propose two recovery s…
A number of applications in engineering, social sciences, physics, and biology involve inference over networks. In this context, graph signals are widely encountered as descriptors of vertex attributes or features in graph-structured data. Estimating such signals in all vertices given noisy observations of their values…
Neural networks outperform NTK on compositional tasks, revealing a complexity gap.
The aim of this paper is to propose distributed strategies for adaptive learning of signals defined over graphs. Assuming the graph signal to be bandlimited, the method enables distributed reconstruction, with guaranteed performance in terms of mean-square error, and tracking from a limited number of sampled observatio…
We study the problem of sampling a bandlimited graph signal in the presence of noise, where the objective is to select a node subset of prescribed cardinality that minimizes the signal reconstruction mean squared error (MSE). To that end, we formulate the task at hand as the minimization of MSE subject to binary constr…
In this paper, we study the adversarial attack and defence problem in deep learning from the perspective of Fourier analysis. We first explicitly compute the Fourier transform of deep ReLU neural networks and show that there exist decaying but non-zero high frequency components in the Fourier spectrum of neural network…
This paper focuses on spectral filters on graphs, namely filters defined as elementwise multiplication in the frequency domain of a graph. In many graph signal processing settings, it is important to transfer a filter from one graph to another. One example is in graph convolutional neural networks (ConvNets), where the…
A new SOHP filter improves trend estimation in economic time series.
Deep density methods improve filtering in high-dimensional systems.
The sophisticated structure of Convolutional Neural Network (CNN) allows for outstanding performance, but at the cost of intensive computation. As significant redundancies inevitably present in such a structure, many works have been proposed to prune the convolutional filters for computation cost reduction. Although ex…
Gradient filters track moving parameters under noisy data and misspecification.
We simplify Bayesian filtering by framing it as optimization, making it practical for high-dimensional systems.
Develops an inverse particle filter for cognitive systems.
Convolutional neural networks (CNNs) achieve state-of-the-art performance in a wide variety of tasks in computer vision. However, interpreting CNNs still remains a challenge. This is mainly due to the large number of parameters in these networks. Here, we investigate the role of compression and particularly pruning fil…
A novel method reduces dimensionality for filtering SRNs with observed variables.
Kernel learning FBSDE filter improves nonlinear filtering efficiency.
New method filters large networks from financial data to reveal key subnetworks.
Many nonlinear extensions of the Kalman filter, e.g., the extended and the unscented Kalman filter, reduce the state densities to Gaussian densities. This approximation gives sufficient results in many cases. However, this filters only estimate states that are correlated with the observation. Therefore, sequential esti…
Paper proves convergence of Kalman filter on Stiefel manifolds with measurement errors.
Improved Kalman filter for non-linear, non-Gaussian data.
This work analyzes the stability of graph filters under large perturbations.
Advances deep network embedding through multi-filtering GCN.
This work preserves linear invariants in ensemble filters for non-Gaussian data assimilation.
Convolutional Bayesian filtering generalizes state estimation by incorporating inequality conditions.
EnSF improves accuracy in tracking high-dimensional nonlinear systems.
Improved Kalman filter for Stiefel manifold measurements.
Latent FxLMS accelerates ANC by adapting along low-dimensional filter weights.
In this paper we introduce a projection method for the space of probability distributions based on the differential geometric approach to statistics. This method is based on a direct L2 metric as opposed to the usual Hellinger distance and the related Fisher Information metric. We explain how this apparatus can be used…
Robust Kalman filtering method for outlier detection.
Recent work has suggested enhancing Bloom filters by using a pre-filter, based on applying machine learning to determine a function that models the data set the Bloom filter is meant to represent. Here we model such learned Bloom filters,, with the following outcomes: (1) we clarify what guarantees can and cannot be as…
Quantifies polynomial approximation rates for smooth functions under various distributions.
This paper presents the construction of a particle filter, which incorporates elements inspired by genetic algorithms, in order to achieve accelerated adaptation of the estimated posterior distribution to changes in model parameters. Specifically, the filter is designed for the situation where the subsequent data in on…
Develops inverse unscented Kalman filter for non-linear systems.
New sampling-based approach for filtering problems using multiplicative Gaussian functions.
Filtering data with a pre-trained model improves multimodal contrastive learning performance.
A new filter reduces density fitting to a linear solve, improving performance on nonlinear systems.
In an effort to understand the meaning of the intermediate representations captured by deep networks, recent papers have tried to associate specific semantic concepts to individual neural network filter responses, where interesting correlations are often found, largely by focusing on extremal filter responses. In this …
HKF uses neural networks to adapt Kalman filters for dynamic channel tracking.
Triangular, overlapping Mel-scaled filters ("f-banks") are the current standard input for acoustic models that exploit their input's time-frequency geometry, because they provide a psycho-acoustically motivated time-frequency geometry for a speech signal. F-bank coefficients are provably robust to small deformations in…
A new ML-based filter improves data assimilation for nonlinear systems.