This paper proposes a new methodology to compute Value at Risk (VaR) for quantifying losses in credit portfolios. We approximate the cumulative distribution of the loss function by a finite combination of Haar wavelets basis functions and calculate the coefficients of the approximation by inverting its Laplace transfor…
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10 results for “Haar-wavelet”
This paper presents a basic property of region dividing of ReLU (rectified linear unit) deep learning when new layers are successively added, by which two new perspectives of interpreting deep learning are given. The first is related to decision trees and forests; we construct a deep learning structure equivalent to a …
The paper reformulates U-Nets as wavelet-based models and applies this to hierarchical VAEs.
problem Theoretical understanding and regularization properties of U-Nets and their relationship to wavelets.
method Formulating a multi-resolution framework to identify U-Nets as finite-dimensional truncations of infinite-dimensional models, proving average pooling corresponds to projection, and identifying HVAEs as discretizations of multi-resolution diffusion processes.
result HVAEs learn a time representation allowing for improved parameter efficiency through weight-sharing.
We present a powerful new loss function and training scheme for learning binary hash functions. In particular, we demonstrate our method by creating for the first time a neural network that outperforms state-of-the-art Haar wavelets and color layout descriptors at the task of automated scene matching. By accurately rel…
The paper improves on existing algorithms for minimizing different types of regret in online learning.
problem Minimizing external, internal, and swap regret in online learning with multiple experts.
method Develops a single algorithm using φ-regret minimization and Haar-wavelet-inspired matrix features to achieve optimal bounds in various scenarios.
result Achieves optimal bounds for external, internal, and swap regrets in different expert scenarios.
The aim of this paper is to discuss the use of Haar scattering networks, which is a very simple architecture that naturally supports a large number of stacked layers, yet with very few parameters, in a relatively broad set of pattern recognition problems, including regression and classification tasks. This architecture…
We propose a new outline for adaptive dictionary learning methods for sparse encoding based on a hierarchical clustering of the training data. Through recursive application of a clustering method, the data is organized into a binary partition tree representing a multiscale structure. The dictionary atoms are defined ad…
Haar Graph Poolingcs.LG
Deep Graph Neural Networks (GNNs) are useful models for graph classification and graph-based regression tasks. In these tasks, graph pooling is a critical ingredient by which GNNs adapt to input graphs of varying size and structure. We propose a new graph pooling operation based on compressive Haar transforms -- HaarPo…
Simplifies and optimizes learning from untrusted batches with structure.
problem Learning from untrusted batches with potential structure.
method Synthesizes techniques from JO19 and CLM19, using Haar wavelets and soft filtering.
result Achieves sublinear sample complexity with polynomial time complexity.
We consider the problem of online forecasting of sequences of length with total-variation at most using observations contaminated by independent -subgaussian noise. We design an -time algorithm that achieves a cumulative square error of with high pro…