Searcharxiv⌕ Search

arXiv subjects

Muhammad Farooq

Publications and source records attributed to Muhammad Farooq.

29 records · Page 2Linked to original sources

COVID-ResNet: A Deep Learning Framework for Screening of COVID19 from Radiographs

In the last few months, the novel COVID19 pandemic has spread all over the world. Due to its easy transmission, developing techniques to accurately and easily identify the presence of COVID19 and distinguish it from other forms of flu and pneumonia is crucial. Recent research has shown that the chest Xrays of patients suffering from COVID19 depicts certain abnormalities in the radiography. However, those approaches are closed source and not made available to the research community for re-producibility and gaining deeper insight. The goal of this work is to build open source and open access datasets and present an accurate Convolutional Neural Network framework for differentiating COVID19 cases from other pneumonia cases. Our work utilizes state of the art training techniques including progressive resizing, cyclical learning rate finding and discriminative learning rates to training fast and accurate residual neural networks. Using these techniques, we showed the state of the art results on the open-access COVID-19 dataset. This work presents a 3-step technique to fine-tune a pre-trained ResNet-50 architecture to improve model performance and reduce training time. We call it COVIDResNet. This is achieved through progressively re-sizing of input images to 128x128x3, 224x224x3, and 229x229x3 pixels and fine-tuning the network at each stage. This approach along with the automatic learning rate selection enabled us to achieve the state of the art accuracy of 96.23% (on all the classes) on the COVIDx dataset with only 41 epochs. This work presented a computationally efficient and highly accurate model for multi-class classification of three different infection types from along with Normal individuals. This model can help in the early screening of COVID19 cases and help reduce the burden on healthcare systems.

eess.IV↗

Learning Rates for Kernel-Based Expectile Regression

Conditional expectiles are becoming an increasingly important tool in finance as well as in other areas of applications. We analyse a support vector machine type approach for estimating conditional expectiles and establish learning rates that are minimax optimal modulo a logarithmic factor if Gaussian RBF kernels are used and the desired expectile is smooth in a Besov sense. As a special case, our learning rates improve the best known rates for kernel-based least squares regression in this scenario. Key ingredients of our statistical analysis are a general calibration inequality for the asymmetric least squares loss, a corresponding variance bound as well as an improved entropy number bound for Gaussian RBF kernels.

stat.ML↗

An SVM-like Approach for Expectile Regression

Expectile regression is a nice tool for investigating conditional distributions beyond the conditional mean. It is well-known that expectiles can be described with the help of the asymmetric least square loss function, and this link makes it possible to estimate expectiles in a non-parametric framework by a support vector machine like approach. In this work we develop an efficient sequential-minimal-optimization-based solver for the underlying optimization problem. The behavior of the solver is investigated by conducting various experiments and the results are compared with the recent R-package ER-Boost.

stat.CO↗

A new Lanczos type algorithm for system of linear equations

Lanczos-type algorithms are efficient and easy to implement. Unfortunately they breakdown frequently and well before convergence has been achieved. These algorithms are typically based on recurrence relations which involve formal orthogonal polynomials of low degree. In this paper, we consider a recurrence relation that has not been studied before and which involves a relatively higher degree polynomial. Interestingly, it leads to an algorithm that shows superior stability when compared to existing Lanczos-type algorithms. This new algorithm is derived and described. It is then compared to the best known algorithms of this type, namely A5/B10, A8/B10, as well as Arnoldi's algorithm, on a set of standard test problems. Numerical results are included.

math.NA↗

A Switching Approach to Avoid Breakdown in Lanczos-type Algorithms

Lanczos-type algorithms are well known for their inherent instability. They typically breakdown when relevant orthogonal polynomials do not exist. Current approaches to avoiding breakdown rely on jumping over the non-existent polynomials to resume computation. This jumping strategy may have to be used many times during the solution process. We suggest an alternative to jumping which consists in switching between different algorithms that have been generated using different recurrence relations between orthogonal polynomials. This approach can be implemented as three different strategies: ST1, ST2, and ST3. We shall briefly recall how Lanczos-type algorithms are derived. Four of the most prominent such algorithms namely $A_4$, $A_{12}$, $A_5/B_{10}$ and $A_5/B_8$ will be presented and then deployed in the switching framework. In this paper, only strategy ST2 will be investigated. Numerical results will be presented.

math.NA↗

Application of fuzzy Laplace transforms for solving fuzzy partial Volterra integro-differential equations

Fuzzy partial integro-differential equations have a major role in the fields of science and engineering. In this paper, we propose the solution of fuzzy partial Volterra integro-differential equation with convolution type kernel using fuzzy Laplace transform method (FLTM) under Hukuhara differentiability. It is shown that FLTM is a simple and reliable approach for solving such equations analytically. Finally, the method is illustrated with few examples to show the ability of the proposed method.

math.GM↗

Solving fuzzy convolution Volterra integro-differential equation via fuzzy Laplace transforms

The solution of integro-differential equations have a major role in the fields of science and engineering. Different approaches both numerical and analytic are used to solve these type of equations. In this paper, the solution of fuzzy convolution Volterra integro-differential equation is investigated using fuzzy Laplace transform method under generalized Hukuhara differentiability. Finally, the method is illustrated with few examples to show the ability of the proposed method.

math.GM↗

New Recurrence Relationships between Orthogonal Polynomials which Lead to New Lanczos-type Algorithms

Lanczos methods for solving $\textit{A}\textbf{x}=\textbf{b}$ consist in constructing a sequence of vectors $(\textbf{x}_k), k=1,...$ such that $\textbf{r}_{k}=\textbf{b}-\textit{A}\textbf{x}_{k}=\textit{P}_{k}(\textit{A})\textbf{r}_{0}$,, where $\textit{P}_{k}$ is the orthogonal polynomial of degree at most $k$ with respect to the linear functional $c$ defined as $c(ξ^i)=(\textbf{y},\textit{A}^i\textbf{r}_{0})$. Let $\textit{P}^{(1)}_{k}$ be the regular monic polynomial of degree $k$ belonging to the family of formal orthogonal polynomials (FOP) with respect to $c^{(1)}$ defined as $c^{(1)}(ξ^{i})=c(ξ^{i+1})$. All Lanczos-type algorithms are characterized by the choice of one or two recurrence relationships, one for $\textit{P}_{k}$ and one for $\textit{P}^{(1)}_{k}$. We shall study some new recurrence relations involving $\textit{P}_{k}$ and $\textit{P}^{(1)}_{k}$ and their possible combination to obtain new Lanczos-type algorithms. We will show that some recurrence relations exist, but cannot be used to derive Lanczos-type algorithms, while others do not exist at all.

math.NA↗

An alternative derivation of a new Lanczos-type algorithm for systems of linear equations

Various recurrence relations between formal orthogonal polynomials can be used to derive Lanczos-type algorithms. In this paper, we consider recurrence relation $A_{12}$ for the choice $U_i(x)=P_i(x)$, where $U_i$ is an auxiliary family of polynomials of exact degree $i$. It leads to a Lanczos-type algorithm that shows superior stability when compared to existing Lanczos-type algorithms. The new algorithm is derived and described. It is then computationally compared to the most robust algorithms of this type, namely $A_{12}$, $A_5/B_{10}$ and $A_8/B_{10}$, on the same test problems. Numerical results are included.

math.NA↗

Solving nth order fuzzy differential equation by fuzzy Laplace transform

In this paper, we generalize the fuzzy Laplace transformation (FLT) for the nth derivative of a fuzzy-valued function named as nth derivative theorem and under the strongly generalized differentiability concept, we use it in an analytical solution method for the solution of an nth order fuzzy initial value problem (FIVP). This is a simple approach toward the solution of nth order fuzzy initial value problem (FIVP) by the nth generalized (FLT) form, and then we can use it to solve any order of FIVP. The related theorems and properties are proved. The method is illustrated with the help of some examples. We use MATLAB to evaluate the inverse Laplace transform.

math.GM↗

Solving fuzzy two-point boundary value problem using fuzzy Laplace transform

A natural way to model dynamic systems under uncertainty is to use fuzzy boundary value problems (FBVPs) and related uncertain systems. In this paper we use fuzzy Laplace transform to find the solution of two-point boundary value under generalized Hukuhara differentiability. We illustrate the method for the solution of the well known two-point boundary value problem Schrodinger equation, and homogeneous boundary value problem. Consequently, we investigate the solutions of FBVPs under as a new application of fuzzy Laplace transform.

math.GM↗