arXiv subjects

Rafał Nowak

Publications and source records attributed to Rafał Nowak.

6 recordsLinked to original sources

arXiv2026

Reducing Estimation Uncertainty Using Normalizing Flows and Stratification

Estimating the expectation of a real-valued function of a random variable from sample data is a critical aspect of statistical analysis, with far-reaching implications in various applications. Current methodologies typically assume (semi-)parametric distributions such as Gaussian or mixed Gaussian, leading to significant estimation uncertainty if these assumptions do not hold. We propose a flow-based model, integrated with stratified sampling, that leverages a parametrized neural network to offer greater flexibility in modeling unknown data distributions, thereby mitigating this limitation. Our model shows a marked reduction in estimation uncertainty across multiple datasets, including high-dimensional (30 and 128) ones, outperforming crude Monte Carlo estimators and Gaussian mixture models. Reproducible code is available at https://github.com/rnoxy/flowstrat.

cs.LG↗

arXiv2020

Plugin Networks for Inference under Partial Evidence

In this paper, we propose a novel method to incorporate partial evidence in the inference of deep convolutional neural networks. Contrary to the existing, top performing methods, which either iteratively modify the input of the network or exploit external label taxonomy to take the partial evidence into account, we add separate network modules ("Plugin Networks") to the intermediate layers of a pre-trained convolutional network. The goal of these modules is to incorporate additional signal, ie information about known labels, into the inference procedure and adjust the predicted output accordingly. Since the attached plugins have a simple structure, consisting of only fully connected layers, we drastically reduced the computational cost of training and inference. At the same time, the proposed architecture allows to propagate information about known labels directly to the intermediate layers to improve the final representation. Extensive evaluation of the proposed method confirms that our Plugin Networks outperform the state-of-the-art in a variety of tasks, including scene categorization, multi-label image annotation, and semantic segmentation.

cs.CV↗

arXiv2019

Adversarial Autoencoders for Compact Representations of 3D Point Clouds

Deep generative architectures provide a way to model not only images but also complex, 3-dimensional objects, such as point clouds. In this work, we present a novel method to obtain meaningful representations of 3D shapes that can be used for challenging tasks including 3D points generation, reconstruction, compression, and clustering. Contrary to existing methods for 3D point cloud generation that train separate decoupled models for representation learning and generation, our approach is the first end-to-end solution that allows to simultaneously learn a latent space of representation and generate 3D shape out of it. Moreover, our model is capable of learning meaningful compact binary descriptors with adversarial training conducted on a latent space. To achieve this goal, we extend a deep Adversarial Autoencoder model (AAE) to accept 3D input and create 3D output. Thanks to our end-to-end training regime, the resulting method called 3D Adversarial Autoencoder (3dAAE) obtains either binary or continuous latent space that covers a much wider portion of training data distribution. Finally, our quantitative evaluation shows that 3dAAE provides state-of-the-art results for 3D points clustering and 3D object retrieval.

cs.LG↗

arXiv2018

Convergence acceleration of alternating series

We propose a new simple convergence acceleration method for wide range class of convergent alternating series. It has some common features with Smith's and Ford's modification of Levin's and Weniger's sequence transformations, but its computational and memory cost is lower. We compare all three methods and give some common theoretical results. Numerical examples confirm a similar performance of all of them.

math.NA↗

arXiv2016

New properties of a certain method of summation of generalized hypergeometric series

In a recent paper (Appl. Math. Comput. 215, 1622--1645, 2009), the authors proposed a method of summation of some slowly convergent series. The purpose of this note is to give more theoretical analysis for this transformation, including the convergence acceleration theorem in the case of summation of generalized hypergeometric series. Some new theoretical results and illustrative numerical examples are given.

math.NA↗

arXiv2012

On the convergence acceleration of some continued fractions

A well known method for convergence acceleration of continued fraction $\K(a_n/b_n)$ is to use the modified approximants $S_n(ω_n)$ in place of the classical approximants $S_n(0)$, where $ω_n$ are close to tails $f^{(n)}$ of continued fraction. Recently, author proposed a method of iterative character producing tail approximations whose asymptotic expansion's accuracy is improving in each step. This method can be applied to continued fractions $\K(a_n/b_n)$, where $a_n$, $b_n$ are polynomials in $n$ ($°a_n=2$, $°b_n\leq 1$) for sufficiently large $n$. The purpose of this paper is to extend this idea for the class of continued fractions $\K(a_n/b_n + a_n'/b_n')$, where $a_n$, $a_n'$, $b_n$, $b_n'$ are polynomials in $n$ ($°a_n=°a_n', °b_n=°b_n'$). We give examples involving such continued fraction expansions of some mathematical constants, as well as elementary and special functions.

math.NA↗