Rectangular Kernel Research Articles

Credit scoring analysis using weighted k nearest neighbor

Credit scoring is a quatitative method to evaluate the credit risk of loan applications. Both statistical methods and artificial intelligence are often used by credit analysts to help them decide whether the applicants are worthy of credit. These methods aim to predict future behavior in terms of credit risk based on past experience of customers with similar characteristics. This paper reviews the weighted k nearest neighbor (WKNN) method for credit assessment by considering the use of some kernels. We use credit data from a private bank in Indonesia. The result shows that the Gaussian kernel and rectangular kernel have a better performance based on the value of percentage corrected classified whose value is 82.4% respectively.

Chimera states in two-dimensional networks of locally coupled oscillators

Chimera state is defined as a mixed type of collective state in which synchronized and desynchronized subpopulations of a network of coupled oscillators coexist and the appearance of such anomalous behavior has strong connection to diverse neuronal developments. Most of the previous studies on chimera states are not extensively done in two-dimensional ensembles of coupled oscillators by taking neuronal systems with nonlinear coupling function into account while such ensembles of oscillators are more realistic from a neurobiological point of view. In this paper, we report the emergence and existence of chimera states by considering locally coupled two-dimensional networks of identical oscillators where each node is interacting through nonlinear coupling function. This is in contrast with the existence of chimera states in two-dimensional nonlocally coupled oscillators with rectangular kernel in the coupling function. We find that the presence of nonlinearity in the coupling function plays a key role to produce chimera states in two-dimensional locally coupled oscillators. We analytically verify explicitly in the case of a network of coupled Stuart-Landau oscillators in two dimensions that the obtained results using Ott-Antonsen approach and our analytical finding very well matches with the numerical results. Next, we consider another type of important nonlinear coupling function which exists in neuronal systems, namely chemical synaptic function, through which the nearest-neighbor (locally coupled) neurons interact with each other. It is shown that such synaptic interacting function promotes the emergence of chimera states in two-dimensional lattices of locally coupled neuronal oscillators. In numerical simulations, we consider two paradigmatic neuronal oscillators, namely Hindmarsh-Rose neuron model and Rulkov map for each node which exhibit bursting dynamics. By associating various spatiotemporal behaviors and snapshots at particular times, we study the chimera states in detail over a large range of coupling parameter. The existence of chimera states is confirmed by instantaneous angular frequency, order parameter and strength of incoherence.

Development of a Finite Volume Particle Method for 3-D fluid flow simulations

The Finite Volume Particle Method (FVPM) is a meshless method for simulating fluid flows which includes many of the desirable features of mesh-based finite volume methods. FVPM benefits from particle interaction vectors to weight conservative fluxes exchanged between particles. These vectors are equivalent to the intercell area vectors in mesh-based finite volume methods. To compute the interaction vectors, either numerical or exact integration has been used. Numerical integration, based on quadrature rules, is approximate and costly, whereas the exact method, employing a top-hat kernel, is precise and fast. To date, quadrature integration has not been used in 3-D due to its excessive cost and the exact method has been developed only for 2-D computations. In this study, we develop a new 3-D FVPM formulation which features a rectangular top-hat kernel to compute interaction vectors exactly and efficiently. We also introduce a new boundary condition enforcement technique based on a single layer of boundary particles. In this technique, no-slip wall boundary conditions with complex geometries are precisely enforced by overlaying a layer of particles on wall surfaces. Employing AUSM+ for inviscid fluxes, weakly-compressible fluid flow is studied with the proposed method. To achieve more accurate results, the solution can be refined near the wall boundary by splitting the fluid particles. This formulation is validated for lid-driven cavity flow, a moving square and jet impingement test cases.

On simplified global nonlinear function for fitness landscape: a case study of inverse protein folding.

The construction of fitness landscape has broad implication in understanding molecular evolution, cellular epigenetic state, and protein structures. We studied the problem of constructing fitness landscape of inverse protein folding or protein design, with the aim to generate amino acid sequences that would fold into an a priori determined structural fold which would enable engineering novel or enhanced biochemistry. For this task, an effective fitness function should allow identification of correct sequences that would fold into the desired structure. In this study, we showed that nonlinear fitness function for protein design can be constructed using a rectangular kernel with a basis set of proteins and decoys chosen a priori. The full landscape for a large number of protein folds can be captured using only 480 native proteins and 3,200 non-protein decoys via a finite Newton method. A blind test of a simplified version of fitness function for sequence design was carried out to discriminate simultaneously 428 native sequences not homologous to any training proteins from 11 million challenging protein-like decoys. This simplified function correctly classified 408 native sequences (20 misclassifications, 95% correct rate), which outperforms several other statistical linear scoring function and optimized linear function. Our results further suggested that for the task of global sequence design of 428 selected proteins, the search space of protein shape and sequence can be effectively parametrized with just about 3,680 carefully chosen basis set of proteins and decoys, and we showed in addition that the overall landscape is not overly sensitive to the specific choice of this set. Our results can be generalized to construct other types of fitness landscape.

Inferring higher-order correlations from filtered spike activity

Event Abstract Back to Event Inferring higher-order correlations from filtered spike activity Imke C. Reimer1*, Benjamin Staude1 and Stefan Rotter1 1 Albert-Ludwig University, Bernstein Center Freiburg & Faculty of Biology, Germany Nonlinear response properties turn neurons into highly sensitive detectors for higher-order features of their input (see e.g. [1]). Whether or not higher-order correlations are important for cortical information processing, however, can only be decided by the analysis of experimental data. Common data analysis methods (e.g. [2]) to investigate the potential role of higher-order correlations (HOCs) are devised for the application to spike recordings from multiple single neurons. A recent particularly promising approach is the cumulant based inference of higher-order correlations (CuBIC, [3]). CuBIC allows to infer a lower bound on the maximal order of correlations by employing the cumulants of the population spike count, i.e. the population spike activity “filtered” with a rectangular kernel. Compared to other methods, this approach can detect even weak HOCs in the activity of large neuronal populations based on realistic sample sizes. However, describing HOCs in a neuronal population does not reveal its influence on the activity of a neuron at the next processing stage. In this respect, estimating cooperative dynamics in the presynaptic spike activity from an intracellular recording of a single neuron would be advantageous (cf. [4] for an approach based on pairwise correlations). To approach this issue, we represent the subthreshold activity as presynaptic activity filtered with a fixed kernel and adapt CuBIC accordingly. Studies on surrogate data revealed that the new method can reliably infer HOCs even from short stretches of membrane potentials. Acknowledgements Support by the German Federal Ministry of Education and Research (BMBF; grant 01GQ0420 to BCCN Freiburg) is gratefully acknowledged.

Detecting Statistically Significant Common Insertion Sites in Retroviral Insertional Mutagenesis Screens

Retroviral insertional mutagenesis screens, which identify genes involved in tumor development in mice, have yielded a substantial number of retroviral integration sites, and this number is expected to grow substantially due to the introduction of high-throughput screening techniques. The data of various retroviral insertional mutagenesis screens are compiled in the publicly available Retroviral Tagged Cancer Gene Database (RTCGD). Integrally analyzing these screens for the presence of common insertion sites (CISs, i.e., regions in the genome that have been hit by viral insertions in multiple independent tumors significantly more than expected by chance) requires an approach that corrects for the increased probability of finding false CISs as the amount of available data increases. Moreover, significance estimates of CISs should be established taking into account both the noise, arising from the random nature of the insertion process, as well as the bias, stemming from preferential insertion sites present in the genome and the data retrieval methodology. We introduce a framework, the kernel convolution (KC) framework, to find CISs in a noisy and biased environment using a predefined significance level while controlling the family-wise error (FWE) (the probability of detecting false CISs). Where previous methods use one, two, or three predetermined fixed scales, our method is capable of operating at any biologically relevant scale. This creates the possibility to analyze the CISs in a scale space by varying the width of the CISs, providing new insights in the behavior of CISs across multiple scales. Our method also features the possibility of including models for background bias. Using simulated data, we evaluate the KC framework using three kernel functions, the Gaussian, triangular, and rectangular kernel function. We applied the Gaussian KC to the data from the combined set of screens in the RTCGD and found that 53% of the CISs do not reach the significance threshold in this combined setting. Still, with the FWE under control, application of our method resulted in the discovery of eight novel CISs, which each have a probability less than 5% of being false detections.

10.1162/153244303765208403

A finite concave minimization algorithm is proposed for constructing kernel classifiers that use a minimal number of data points both in generating and characterizing a classifier. The algorithm is theoretically justified on the basis of linear programming perturbation theory and a leave-one-out error bound as well as effective computational results on seven real world datasets. A nonlinear rectangular kernel is generated by systematically utilizing as few of the data as possible both in training and in characterizing a nonlinear separating surface. This can result in substantial reduction in kernel data-dependence (over 94% in six of the seven public datasets tested on) and with test set correctness equal to that obtained by using a conventional support vector machine classifier that depends on many more data points. This reduction in data dependence results in a much faster classifier that requires less storage. To eliminate data points, the proposed approach makes use of a novel loss function, the pound function (·)#, which is a linear combination of the 1-norm and the step function that measures both the magnitude and the presence of any error.

Improved Estimators in Nonparametric Regression Problems

Linear estimators of multivariate means are considered. Generalizations of some well-known theorems about admissibility of linear estimators are given. The results then are applied to show that commonly used kernel-type estimators in nonparametric regression problems can be constructively improved in a simple way. An asymptotic result is described that gives a quantitative measure of the maximum improvement to be gained in certain situations. A theoretical bound shows that gains are achievable in the relative risk of up to 58.6% (rectangular kernel) or 29.2% (Epanechnikov kernel). Some examples of smaller sample size are also investigated, and these show relative risk gains ranging up to 18% in realistic settings.

Quadratic mode regression

Abstract Generalizing the mode regression of Lee (1989) with the rectangular kernel (RME), we try a quadratic kernel (QME), smoothing the rectangular kernel. Like RME, QME is the most useful when the dependent variable is truncated. QME is better than RME in that it gives a N 1 2 - consistent estimator and an asymptotic distribution which parallels that of Powell's (1986) symmetrically trimmed least squares (STLS). In general, the symmetry requirement of QME is weaker than that of STLS and stronger than that of RME. Estimation of the covariance matrices of both QME and STLS requires density estimation. But a variation of QME can provide an upper bound of the covariance matrix without the burden of density estimation. The upper bound can be made tight at the cost of computation time.