Consistency of logistic classifier in abstract Hilbert spaces

We study the asymptotic behavior of the logistic classifier in an abstract Hilbert space and require realistic conditions on the distribution of data for its consistency. The number kn of estimated parameters via maximum quasi-likelihood is allowed to diverge so that kn/n → 0 and nτ 4 kn → ∞, where n is the number of observations and τkn is the variance of the last principal component of data used for estimation. This is the only result on the consistency of the logistic classifier we know so far when the data are assumed to come from a Hilbert space

A study of logistic classifier: uniform consistency in finite-dimensional linear spaces

Let X be a random variable taking values in a finite dimensional linear space and Y ∈ {0, 1} its associated label. We study the case, where conditional distribution p(x) = P(Y = 1 | X = x) depends on x through some linear form θx. We show that in this case, under a mild assumption on the distribution µ of X, a maximum-likelihood estimator pˆ, as well as the induced class of logistic classifiers, are uniformly (w.r.t. p) consistent

Conditions for Existence of Uniformly Consistent Classifiers

We consider the statistical problem of binary classification, which means attaching a random observation X from a separable metric space E to one of the two classes, 0 or 1. We prove that the consistent estimation of conditional probability p(X)= P(Y=1 X) , where Y is the true class of X, is equivalent to the consistency of a class of empirical classifiers. We then investigate for what classes P there exist an estimate p that is consistent uniformly in p P. We show that this holds if and only if P is a totally bounded subset of L1(Eμ), where μ is the distribution of X. In the case, where E is countable, we give a complete characterization of classes π, allowing consistent estimation of p, uniform in (μ,p)ϵπ

Identification of mycolic acid forms using surface-enhanced Raman scattering as a fast detection method for tuberculosis

Background: Tuberculosis (TB) is the ninth leading cause of death worldwide and the leading cause from a single infectious agent, based on the WHO Global Tuberculosis Report in 2017. TB causes massive health care burdens in many parts of the world, specifically in the resource constrained developing world. Most deaths from TB could be prevented with cost effective early diagnosis and appropriate treatment. Purpose: Conventional TB detection methods are either too slow as it takes a few weeks for diagnosis or they lack the specificity and accuracy. Thus the objective of this study was to develop a fast and efficient detection for TB using surface enhanced Raman scattering (SERS) technique. Methods: SERS spectra for different forms of mycolic acids (MAs) that are both synthetic origin and actual extracts from the mycobacteria species were obtained by label-free direct detection mode. Similarly, we collected SERS spectra for γ-irradiated whole bacteria (WB). Measurements were done using silver (Ag) coated silicon nanopillar (Ag SNP) as SERS substrate. Results: We report the SERS based detection of MA, which is a biomarker for mycobacteria species including Mycobacterium tuberculosis. For the first time, we also establish the SERS spectral characterization of the three major forms of MA – αMA, methoxy-MA, and keto-MA, in bacterial extracts and also in γ-irradiated WB. We validated our findings by mass spectrometry. SERS detection of these three forms of MA could be useful in differentiating pathogenic and nonpathogenic Mycobacterium spp. Conclusions: We have demonstrated the direct detection of three major forms of MA – αMA, methoxy-MA, and keto-MA, in two different types of MA extracts from MTB bacteria, namely delipidated MA and undelipidated MA and finally in γ-irradiated WB. In the near future, this study could pave the way for a fast and efficient detection method for TB, which is of high clinical significance

SERS-based detection of haptoglobin in ovarian cyst fluid as a point-of-care diagnostic assay for epithelial ovarian cancer

Purpose: To evaluate haptoglobin (Hp) in ovarian cyst fluid as a diagnostic biomarker for epithelial ovarian cancers (EOCs) using surface-enhanced Raman spectroscopy (SERS)-based in vitro diagnostic assay for use in an intraoperative setting. Methods: SERS-based method was used to detect and quantify Hp in archived ovarian cyst fluids collected from suspicious ovarian cysts and differentiate benign tumors from EOCs. The diagnostic performance of SERS-based assay was verified against the histopathology conclusions and compared with the results of CA125 test and frozen sections. Results: Hp concentration present in the clinical cyst fluid measured by SERS was normalized to 3.3 mg/mL of standard Hp. Normalized mean values for patients with benign cysts were 0.65 (n=57) and malignant cysts were 1.85 (n=54), demonstrating a significantly (P<0.01) higher Hp in malignant samples. Verified against histology, Hp measurements using SERS had a sensitivity of 94% and specificity of 91%. Receiver operating characteristic curve analysis of SERS-based Hp measurements resulted in area under the curve of 0.966±0.03, establishing the robustness of the method. CA125 test on the same set of patients had a sensitivity of 85% and specificity of 90%, while frozen section analysis on 65 samples had 100% sensitivity and specificity. Conclusion: With a total execution time of <10 minutes and consistent performance across different stages of cancer, the SERS-based Hp detection assay can serve as a promising intraoperative EOC diagnostic test.National Medical Research Council (NMRC), Singapore; Bio-Medical Research Council of Agency for Science, Technology and Research (A*STAR), and the NHIC Innovation to Develop (I2D

Multispectral Photoacoustic Imaging Artifact Removal and Denoising Using Time Series Model-Based Spectral Noise Estimation

The aim of this study is to solve a problem of denoising and artifact removal from in vivo multispectral photoacoustic imaging when the level of noise is not known a priori. The study analyzes Wiener filtering in Fourier domain when a family of anisotropic shape filters is considered. The unknown noise and signal power spectral densities are estimated using spectral information of images and the autoregressive of the power 1 (AR(1) model. Edge preservation is achieved by detecting image edges in the original and the denoised image and superimposing a weighted contribution of the two edge images to the resulting denoised image. The method is tested on multispectral photoacoustic images from simulations, a tissue-mimicking phantom, as well as in vivo imaging of the mouse, with its performance compared against that of the standard Wiener filtering in Fourier domain. The results reveal better denoising and fine details preservation capabilities of the proposed method when compared to that of the standard Wiener filtering in Fourier domain, suggesting that this could be a useful denoising technique for other multispectral photoacoustic studies

Identification of mycolic acid forms using surface-enhanced Raman scattering as a fast detection method for tuberculosis

Jayakumar Perumal,1 US Dinishm,1 Anne K Bendt,2 Agne Kazakeviciute,1,3 Chit Yaw Fu,1 Irvine Lian Hao Ong,4 Malini Olivo1 1Laboratory of Bio-optical Imaging, Singapore Bioimaging Consortium, Agency for Science, Technology, and Research (A*STAR), Singapore; 2Singapore Lipidomics Incubator, Life Sciences Institute, National University of Singapore, Singapore; 3Department of Statistical Science, University College London, London, UK; 4Matralix Pte Ltd, Singapore Background: Tuberculosis (TB) is the ninth leading cause of death worldwide and the leading cause from a single infectious agent, based on the WHO Global Tuberculosis Report in 2017. TB causes massive health care burdens in many parts of the world, specifically in the resource constrained developing world. Most deaths from TB could be prevented with cost effective early diagnosis and appropriate treatment.Purpose: Conventional TB detection methods are either too slow as it takes a few weeks for diagnosis or they lack the specificity and accuracy. Thus the objective of this study was to develop a fast and efficient detection for TB using surface enhanced Raman scattering (SERS) technique.Methods: SERS spectra for different forms of mycolic acids (MAs) that are both synthetic origin and actual extracts from the mycobacteria species were obtained by label-free direct detection mode. Similarly, we collected SERS spectra for &gamma;-irradiated whole bacteria (WB). Measurements were done using silver (Ag) coated silicon nanopillar (Ag SNP) as SERS substrate.Results: We report the SERS based detection of MA, which is a biomarker for mycobacteria species including Mycobacterium tuberculosis. For the first time, we also establish the SERS spectral characterization of the three major forms of MA &ndash; &alpha;MA, methoxy-MA, and keto-MA, in bacterial extracts and also in &gamma;-irradiated WB. We validated our findings by mass spectrometry. SERS detection of these three forms of MA could be useful in differentiating pathogenic and nonpathogenic Mycobacterium spp.Conclusions: We have demonstrated the direct detection of three major forms of MA &ndash; &alpha;MA, methoxy-MA, and keto-MA, in two different types of MA extracts from MTB bacteria, namely delipidated MA and undelipidated MA and finally in &gamma;-irradiated WB. In the near future, this study could pave the way for a fast and efficient detection method for TB, which is of high clinical significance. Keywords: Mycobacterium tuberculosis, MTB, nontuberculosis mycobacteria, NTM, mycolic acid, MA, SERS, silver-coated silicon nanopillars, Ag SNPs, liquid chromatography mass spectrometry, LC-M

SERS-based detection of haptoglobin in ovarian cyst fluid as a point-of-care diagnostic assay for epithelial ovarian cancer

Jayakumar Perumal,1,* Aniza Puteri Mahyuddin,2,* Ghayathri Balasundaram,1,* Douglas Goh,1 Chit Yaw Fu,1 Agne Kazakeviciute,1,3 US Dinish,1 Mahesh Choolani,2 Malini Olivo1 1Laboratory of Bio-optical Imaging, Singapore Bioimaging Consortium, Agency for Science Technology and Research (A*STAR), Singapore; 2Department of Obstetrics and Gynecology, Yong Loo Lin School of Medicine, National University of Singapore, Singapore; 3Department of Mathematics, Brunel University London, Uxbridge, UK *These authors contributed equally to this work Purpose: To evaluate haptoglobin (Hp) in ovarian cyst fluid as a diagnostic biomarker for epithelial ovarian cancers (EOCs) using surface-enhanced Raman spectroscopy (SERS)-based in vitro diagnostic assay for use in an intraoperative setting. Methods: SERS-based method was used to detect and quantify Hp in archived ovarian cyst fluids collected from suspicious ovarian cysts and differentiate benign tumors from EOCs. The diagnostic performance of SERS-based assay was verified against the histopathology conclusions and compared with the results of CA125 test and frozen sections. Results: Hp concentration present in the clinical cyst fluid measured by SERS was normalized to 3.3 mg/mL of standard Hp. Normalized mean values for patients with benign cysts were 0.65 (n=57) and malignant cysts were 1.85 (n=54), demonstrating a significantly (P&lt;0.01) higher Hp in malignant samples. Verified against histology, Hp measurements using SERS had a sensitivity of 94% and specificity of 91%. Receiver operating characteristic curve analysis of SERS-based Hp measurements resulted in area under the curve of 0.966&plusmn;0.03, establishing the robustness of the method. CA125 test on the same set of patients had a sensitivity of 85% and specificity of 90%, while frozen section analysis on 65 samples had 100% sensitivity and specificity. Conclusion: With a total execution time of&nbsp;&lt;10 minutes and consistent performance across&nbsp;different stages of cancer, the SERS-based Hp detection assay can serve as a promising intraoperative&nbsp;EOC diagnostic test.&nbsp; Keywords: surface-enhanced Raman spectroscopy, haptoglobin, epithelial ovarian cancer, ovarian cyst fluid, point-of-care diagnostic