Identifying somatic fingerprints of cancers defined by germline and environmental risk factors.

Numerous studies over the past generation have identified germline variants that increase specific cancer risks. Simultaneously, a revolution in sequencing technology has permitted high-throughput annotations of somatic genomes characterizing individual tumors. However, examining the relationship between germline variants and somatic alteration patterns is hugely challenged by the large numbers of variants in a typical tumor, the rarity of most individual variants, and the heterogeneity of tumor somatic fingerprints. In this article, we propose statistical methodology that frames the investigation of germline-somatic relationships in an interpretable manner. The method uses meta-features embodying biological contexts of individual somatic alterations to implicitly group rare mutations. Our team has used this technique previously through a multilevel regression model to diagnose with high accuracy tumor site of origin. Herein, we further leverage topic models from computational linguistics to achieve interpretable lower-dimensional embeddings of the meta-features. We demonstrate how the method can identify distinctive somatic profiles linked to specific germline variants or environmental risk factors. We illustrate the method using The Cancer Genome Atlas whole-exome sequencing data to characterize somatic tumor fingerprints in breast cancer patients with germline BRCA1/2 mutations and in head and neck cancer patients exposed to human papillomavirus.

Topical hidden genome: discovering latent cancer mutational topics using a Bayesian multilevel context-learning approach.

Inferring the cancer-type specificities of ultra-rare, genome-wide somatic mutations is an open problem. Traditional statistical methods cannot handle such data due to their ultra-high dimensionality and extreme data sparsity. To harness information in rare mutations, we have recently proposed a formal multilevel multilogistic "hidden genome" model. Through its hierarchical layers, the model condenses information in ultra-rare mutations through meta-features embodying mutation contexts to characterize cancer types. Consistent, scalable point estimation of the model can incorporate 10s of millions of variants across thousands of tumors and permit impressive prediction and attribution. However, principled statistical inference is infeasible due to the volume, correlation, and noninterpretability of mutation contexts. In this paper, we propose a novel framework that leverages topic models from computational linguistics to effectuate dimension reduction of mutation contexts producing interpretable, decorrelated meta-feature topics. We propose an efficient MCMC algorithm for implementation that permits rigorous full Bayesian inference at a scale that is orders of magnitude beyond the capability of existing out-of-the-box inferential high-dimensional multi-class regression methods and software. Applying our model to the Pan Cancer Analysis of Whole Genomes dataset reveals interesting biological insights including somatic mutational topics associated with UV exposure in skin cancer, aging in colorectal cancer, and strong influence of epigenome organization in liver cancer. Under cross-validation, our model demonstrates highly competitive predictive performance against blackbox methods of random forest and deep learning.

How cholesterol stiffens unsaturated lipid membranes.

Cholesterol is an integral component of eukaryotic cell membranes and a key molecule in controlling membrane fluidity, organization, and other physicochemical parameters. It also plays a regulatory function in antibiotic drug resistance and the immune response of cells against viruses, by stabilizing the membrane against structural damage. While it is well understood that, structurally, cholesterol exhibits a densification effect on fluid lipid membranes, its effects on membrane bending rigidity are assumed to be nonuniversal; i.e., cholesterol stiffens saturated lipid membranes, but has no stiffening effect on membranes populated by unsaturated lipids, such as 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC). This observation presents a clear challenge to structure-property relationships and to our understanding of cholesterol-mediated biological functions. Here, using a comprehensive approach-combining neutron spin-echo (NSE) spectroscopy, solid-state deuterium NMR (2H NMR) spectroscopy, and molecular dynamics (MD) simulations-we report that cholesterol locally increases the bending rigidity of DOPC membranes, similar to saturated membranes, by increasing the bilayer's packing density. All three techniques, inherently sensitive to mesoscale bending fluctuations, show up to a threefold increase in effective bending rigidity with increasing cholesterol content approaching a mole fraction of 50%. Our observations are in good agreement with the known effects of cholesterol on the area-compressibility modulus and membrane structure, reaffirming membrane structure-property relationships. The current findings point to a scale-dependent manifestation of membrane properties, highlighting the need to reassess cholesterol's role in controlling membrane bending rigidity over mesoscopic length and time scales of important biological functions, such as viral budding and lipid-protein interactions.

Molecular Recognition Driven Bioinspired Directional Supramolecular Assembly of Amphiphilic (Macro)molecules and Proteins.

Bioinspired self-assembly has been explored with diverse synthetic scaffolds, among which amphiphiles are perhaps the most extensively studied systems. Classical surfactants or amphiphilic block copolymers, depending on the hydrophobic-hydrophilic balance, produce distinct nanostructures, which hold promise for applications ranging from biology to materials sciences. Nevertheless, their immiscibility-driven aggregation does not provide the opportunity to precisely regulate the internal order, morphology, or functional group display, which is highly desirable, especially in the context of biological applications.A new class of amphiphiles have emerged in the recent past in which the hydrophilic segment(s) is appended with a hydrophobic supramolecular-structure-directing-unit (SSDU), consisting of a π-conjugated chromophore and a H-bonding group. Self-recognition of the SSDU by attractive directional interactions governs the supramolecular assembly, which is fundamentally different than the repulsive solvent-immiscibility driven aggregation of traditional amphiphiles. Such SSDU-appended hydrophilic polymers exhibit entropy-driven highly stable self-assembly producing distinct nanostructures depending on the H-bonding functional group. For example, polymers with the hydrazide-functionalized SSDU attached form a polymersome, while in a sharp contrast, the same polymers when connected to an amide containing SSDU produce a cylindrical micelle via a spherical-micelle intermediate. This relationship holds true for a series of SSDU-attached hydrophilic polymers irrespective of the hydrophobic/hydrophilic balance or chemical structure, indicating that the supramolecular-assembly is primarily controlled by the specific molecular-recognition motif of the SSDU, instead of the packing parameter-based norms. Beyond synthetic polymers, SSDU-attached proteins also exhibit similar molecular-recognition driven self-assembly as well as coassembly with SSDU-attached polymers or hydrophilic wedges, producing multi-stimuli-responsive nanostructures in which the protein gains remarkable protection from thermal denaturation or enzymatic hydrolysis and exhibits redox-responsive enzymatic activity.Furthermore, SSDU-derived bola-shape π-amphiphiles have been recognized as a useful scaffold for the synthesis of unsymmetric polymersomes, rarely reported in the literature. The building block consists of a hydrophobic naphthalene-diimide (NDI) π-system attached to a hydrophilic functional group (ionic or nonionic) and a nonionic wedge on its two opposite arms. Extended H-bonding among the hydrazide groups, placed only on one side of the central chromophore by design, ensures stacking of the NDIs with parallel orientation and induces a preferred direction of curvature so that the H-bonded chain and consequently the functional groups attached to the same side remain at the inner-wall of the supramolecular polymersome. Automatically, the functional groups, located on the other side, are displayed at the outer surface. This design works for different amphiphiles, which by virtue of efficient and predictable functional group display, strongly influences the multivalent binding with different biological targets resulting in efficient enzyme inhibition, glycocluster effect, or antibacterial activity, depending on the nature of the functional group. By taking advantage of the electron accepting nature of the NDI, electron rich pyrene-containing amphiphiles can be costacked in alternating sequence, producing temperature and redox-responsive supramolecular polymers with NDI/pyrene stoichiometry-dependent morphology, lower critical solution temperature (LCST), functional group display, and antibacterial activity.

Bayesian analysis of coupled cellular and nuclear trajectories for cell migration.

Cell migration, the process by which cells move from one location to another, plays crucial roles in many biological events. While much research has been devoted to understand the process, most statistical cell migration models rely on using time-lapse microscopy data from cell trajectories alone. However, the cell and its associated nucleus work together to orchestrate cell movement, which motivates a joint analysis of coupled cell-nucleus trajectories. In this paper, we propose a Bayesian hierarchical model for analyzing cell migration. We incorporate a bivariate angular distribution to handle the coupled cell-nucleus trajectories and introduce latent motility status indicators to model a cell's motility as a time-dependent characteristic. A Markov chain Monte Carlo algorithm is provided for practical implementation of our model, which is used on real experimental data from MDA-MB-231 and NIH 3T3 cells. Through the fitted models, deeper insights into the migratory patterns of these experimental cell populations are gained and their differences are quantified.

On the use of the likelihood ratio test methodology in pharmacovigilance.

The safety of medical products due to adverse events (AE) from drugs, therapeutic biologics, and medical devices is a major public health concern worldwide. Likelihood ratio test (LRT) approaches to pharmacovigilance constitute a class of rigorous statistical tools that permit objective identification of AEs of a specific drug and/or a class of drugs cataloged in spontaneous reporting system databases. However, the existing LRT approaches encounter certain theoretical and computational challenges when an underlying Poisson model assumption is violated, including in cases of zero-inflated data. We briefly review existing LRT approaches and propose a novel class of (pseudo-) LRT methods to address these challenges. Our approach uses an alternative parametrization to formulate a unified framework with a common test statistic that can handle both Poisson and zero-inflated Poisson (ZIP) models. The proposed framework is computationally efficient, and it reveals deeper insights into the comparative behaviors of the Poisson and the ZIP models for handling AE data. Our extensive simulation studies document notably superior performances of the proposed methods over existing approaches particularly under zero-inflation, both in terms of statistical (eg, much better control of the nominal level and false discovery rate with substantially enhanced power) and computational ( ∼ $$ \sim $$ 100-500-fold gains in average running times) performance metrics. An application of our method on the statin drug class from the FDA FAERS database reveals interesting insights on potential AEs. An R package, pvLRT, implementing our methods has been released in the public domain.

Longitudinal changes in cardiac function in Duchenne muscular dystrophy population as measured by magnetic resonance imaging.

BACKGROUND: The lack of dystrophin in cardiomyocytes in Duchenne muscular dystrophy (DMD) is associated with progressive decline in cardiac function eventually leading to death by 20-40 years of age. The aim of this prospective study was to determine rate of progressive decline in left ventricular (LV) function in Duchenne muscular dystrophy (DMD) over 5 years. METHODS: Short axis cine and grid tagged images of the LV were acquired in individuals with DMD (n = 59; age = 5.3-18.0 years) yearly, and healthy controls at baseline (n = 16, age = 6.0-18.3 years) on a 3 T MRI scanner. Grid-tagged images were analyzed for composite circumferential strain (ℇcc%) and ℇcc% in six mid LV segments. Cine images were analyzed for left ventricular ejection fraction (LVEF), LV mass (LVM), end-diastolic volume (EDV), end-systolic volume (ESV), LV atrioventricular plane displacement (LVAPD), and circumferential uniformity ratio estimate (CURE). LVM, EDV, and ESV were normalized to body surface area for a normalized index of LVM (LVMI), EDV (EDVI) and ESV (ESVI). RESULTS: At baseline, LV ℇcc% was significantly worse in DMD compared to controls and five of the six mid LV segments demonstrated abnormal strain in DMD. Longitudinal measurements revealed that ℇcc% consistently declined in individuals with DMD with the inferior segments being more affected. LVEF progressively declined between 3 to 5 years post baseline visit. In a multivariate analysis, the use of cardioprotective drugs trended towards positively impacting cardiac measures while loss of ambulation and baseline age were associated with negative impact. Eight out of 17 cardiac parameters reached a minimal clinically important difference with a threshold of 1/3 standard deviation. CONCLUSION: The study shows a worsening of circumferential strain in dystrophic myocardium. The findings emphasize the significance of early and longitudinal assessment of cardiac function in DMD and identify early biomarkers of cardiac dysfunction to help design clinical trials to mitigate cardiac pathology. This study provides valuable non-invasive and non-contrast based natural history data of cardiac changes which can be used to design clinical trials or interpret the results of current trials aimed at mitigating the effects of decreased cardiac function in DMD.

Using the "Hidden" genome to improve classification of cancer types.

It is increasingly common clinically for cancer specimens to be examined using techniques that identify somatic mutations. In principle, these mutational profiles can be used to diagnose the tissue of origin, a critical task for the 3% to 5% of tumors that have an unknown primary site. Diagnosis of primary site is also critical for screening tests that employ circulating DNA. However, most mutations observed in any new tumor are very rarely occurring mutations, and indeed the preponderance of these may never have been observed in any previous recorded tumor. To create a viable diagnostic tool we need to harness the information content in this "hidden genome" of variants for which no direct information is available. To accomplish this we propose a multilevel meta-feature regression to extract the critical information from rare variants in the training data in a way that permits us to also extract diagnostic information from any previously unobserved variants in the new tumor sample. A scalable implementation of the model is obtained by combining a high-dimensional feature screening approach with a group-lasso penalized maximum likelihood approach based on an equivalent mixed-effect representation of the multilevel model. We apply the method to the Cancer Genome Atlas whole-exome sequencing data set including 3702 tumor samples across seven common cancer sites. Results show that our multilevel approach can harness substantial diagnostic information from the hidden genome.

Supramolecular Nanowires from an Acceptor-Donor-Acceptor Conjugated Chromophore.

Oligothiophene derivatives have been extensively studied as p-type semiconducting materials in organic electronics applications. This work reports the synthesis, self-assembly and photophysical properties of acceptor-donor-acceptor (A-D-A)-type oligothiophene derivatives by end-group engineering of quaterthiophene (QT) with naphthalene monoimide (NMI) chromophores that are further connected to a trialkoxy benzamide wedge. Conjugation to the NMI units reduces the HOMO-LUMO gap significantly, and consequently the absorption spectrum exhibits a bathochromic shift of about 50 nm compared with QT. Furthermore, extended H-bonding interactions among the amido groups of the peripheral wedges produce entangled fibrillar nanostructures and gelation in hydrocarbon solvents such as methylcyclohexane, wherein the A-D-A chromophore exhibits typical H-aggregation. On the contrary, the fact that the same chromophore, lacking only the amido units, does not produce gels or H-aggregates indicates strong impact of H-bonding on the self-assembly. Computational studies revealed the electronic properties of the chromophore and predicted the geometry of a dimer in the H-aggregate that reasonably matches with the experimental results. Bulk electrical conductivity measurements determined an excellent conductivity of 2.3×10-2  S cm-1 for the H-aggregated system (OT-1), which is two orders of magnitude higher than that of the same chromophore lacking the amido groups (OT-2).

Multi-Stimuli-Responsive Directional Assembly of an Amphiphilic Donor-Acceptor Alternating Supramolecular Copolymer.

The stimuli-responsive supramolecular co-assembly of two π-amphiphiles, NDI-1 and Py-1, in which an acceptor (A) (naphthalene diimide) and a donor (D) (pyrene) chromophore, respectively, serve as the hydrophobic segment, is described. In addition, both contain an amide group in a designated location so that H-bonding and D-A charge-transfer (CT) interactions can operate simultaneously. H-bonding among the amide groups not only enhanced the CT interaction promoted by the alternating D-A stacking propensity, but also fixed the lateral orientation of the two chromophores and thus compelled the anionic and nonionic hydrophilic head groups, appended with the D and A amphiphiles, respectively, to remain segregated on two opposite sides of the amphiphilic alternating supramolecular copolymer. This copolymer showed spontaneous polymersome assembly with the D-appended anionic groups displayed at the outer surface, whereas the A-appended hydrophilic wedge converged at the inner lacuna. In contrast, spherical or cylindrical micellar structures were produced by Py-1 and NDI-1, respectively. Effective functional-group display in the D-A supramolecular polymersome enabled protein-surface recognition and inhibition of the enzymatic activity of Cht. Under a reducing environment, formation of NDI.- jeopardized the D-A interaction and thus the A chromophores were ejected out of the membrane of the polymersome causing its gradual contraction in size by >75 %. D-A supramolecular polymersomes also exhibited a lower critical solution temperature that could be tuned across a temperature window of 40 to 70 °C by varying the ratio of the A and D components in the alternating supramolecular copolymer.

Phospholipid Bilayer Softening Due to Hydrophobic Gold Nanoparticle Inclusions.

Liposome-nanoparticle assemblies (LNAs) are vital in the context of novel targeted drug-delivery systems, in addition to investigating nanoparticle-lipid bilayer interactions. Quantifying membrane structural properties and dynamics in presence of nanoparticle inclusions provides a simple model to elucidate nanoparticle effects on membrane biophysical properties. We present experimental evidences of bilayer softening due to small hydrophobic gold nanoparticle inclusions. LNA structure has been investigated by a combination of cryo-transmission electron microscopy, dynamic light scattering, and small-angle neutron scattering. Neutron spin echo spectroscopy demonstrated a remarkable ∼15% bending modulus decrease for LNAs relative to pure liposomes. Clear dependence of bending modulus on gold nanoparticle diameter and concentration was observed from our observations. Our findings point toward local bilayer fluidization by nanoparticle inclusions leading to an overall bilayer softening. These findings add valuable information to liposomal drug-delivery vehicle design and membrane biophysics research.

Supramolecularly Engineered π-Amphiphile.

This article describes self-assembly of supramolecularly engineered naphthalene-diimide (NDI)-derived amphiphiles NDI-1 and NDI-2. They have the same hydrophobic/hydrophilic balance but merely differ by a single functional group, amide or ester. They exhibit distinct self-assembly in water; NDI-1 forms hydrogel, which upon aging forms crystals, whereas NDI-2 forms micelles as revealed by in-depth structural analysis using cryo-TEM, dynamic light scattering, and small-angle X-ray scattering studies. These results suggest that the H-bonding among the amide groups fully regulates the self-assembly by overruling the packing parameters. Further, the present study elucidates sharp lower critical solution temperature exhibited by these π-amphiphiles, which has been extensively studied for many important applications of water-soluble polymers but hardly known in the literature of small-molecule surfactants. Control experiments with the same water-soluble hydrophilic wedge did not show such a property, confirming this to be a consequence of the supramolecular polymerization by extended amide-amide H-bonding and not inherent to the structure of the hydrophilic wedge containing oligo-oxyethylene chains.

Rational Design for Complementary Donor-Acceptor Recognition Pairs Using Self-Complementary Hydrogen Bonds.

An adaptable and efficient molecular recognition pair has been established by taking advantage of the complementary nature of donor-acceptor interactions together with the strength of hydrogen bonds. Such distinct molecular recognition propagates in orthogonal directions to effect extended alternating co-assembly of two different appended molecular entities. The dimensions of the assembled structures can be tuned by stoichiometric imbalance between the donor and acceptor building blocks. The morphology of the self-assembled material can be correlated with the ratio of the two building blocks.

Vaporized Δ9-tetrahydrocannabinol exposure in utero has negative effects on attention in a dose- and sex-dependent manner.

There has been an increasing use of cannabis during pregnancy in recent years. Studies have indicated that THC exposure in utero may increase the risk of attention deficits and memory impairments in adolescence. The goal of the present study is to investigate the effects of vaporized THC exposure during pregnancy on offspring memory and attention performance in early and late adolescence. Pregnant dams were exposed to vaporized THC (10 mg or 40 mg) daily from gestational day 2 until labor. Pups were given either a standard or a high-fat diet at weaning and tested in early and late adolescence in two memory tests, the Novel Object Recognition (NOR) test and the Morris Water Maze (MWM) test, and a test of attention, the Object-Based Attention (OBA) test. Rats exposed to low-dose THC showed significantly decreased object exploration in both the NOR and OBA tests, indicating decreased attention. Object exploration time in OBA was significantly lower in females than males. Additionally, post hoc analysis of MWM tests showed some differences in learning patterns for HD THC offspring in early adolescence, possibly due to diet interaction, but ultimate performance was not impacted. While there are existing studies examining prenatal exposure to THC in rodents, this is the first to our knowledge examining memory and attention in adolescence following vaporized THC exposure in utero, and we find indications that prenatal THC exposure may lead to attention deficits and altered memory performance.

Comparison of Surgical Techniques for the Treatment of Congenital Nasal Pyriform Aperture Stenosis: A Systematic Review.

INTRODUCTION: Congenital nasal pyriform aperture stenosis (CNPAS) is a rare condition that results in neonatal respiratory difficulty. The purpose of this systematic review was to compare surgical outcomes of drilling versus dilation techniques in the treatment of CNPAS. METHODS: Pubmed, Embase, and Cochrane Clinical Trials databases were searched for terms "congenital nasal pyriform aperture stenosis" or "pyriform aperture stenosis" from 2010 to 2021. Twenty-five studies were included that evaluated pediatric patients treated surgically for CNPAS with available outcomes data including complications, revisions, and length of stay. RESULTS: A total of 51 patients with CNPAS were pooled from included studies. The median age was 29 days, 56.9% were female, and 54.9% were born full-term. The median pyriform aperture width before surgery was 5.00 mm (IQR = 4.10, 6.45). Forty (78.4%) patients underwent sublabial drilling, while 6 had a dilation procedure performed with hegar cervical dilators, 2 had a balloon dilation, and 3 were dilated with either an acrylic device, endotracheal tube, or bougie. There were no post-operative complications for 76.5% of patients, while a second surgery was required in 9 (17.6%) patients. The median length of stay was 11 days (IQR = 4, 26). No statistically significant difference was observed between sublabial drilling and surgical dilation techniques with respect to complications, need for revision surgery, or length of stay. CONCLUSION: Current literature is insufficient to determine if drilling or dilation is more effective in the treatment of CNPAS.

Vaporized Δ9-THC in utero results in reduced birthweight, increased locomotion, and altered wake-cycle activity dependent on dose, sex, and diet in the offspring.

AIMS: Preclinical studies have found that chronic ∆9-tetrahydrocannabinol (THC) treatment is directly associated with weight gain when introduced during adolescence and adulthood, but the effect of prenatal THC is unclear. Clinical studies have demonstrated prenatal exposure to THC is a prospective predictor of increased health risks associated with obesity. Our study aims to examine prenatal THC impact on obesity risks in males and females throughout adolescence using a clinically relevant inhalation model. METHODS: Pregnant rats were exposed to one of the following from gestational day 2 through birth: 10 mg THC, 40 mg THC, or air. Daily 10-min inhalations were conducted in each animal from 0900 to 1200. Offspring from each treatment group were given either a high-fat diet (HFD) or a normal diet (ND). Food and bodyweights were collected daily, while circadian activity, locomotion, and exercise were measured periodically (PND 21-60). Pregnancy weight gain and birth weight were collected to determine early-life developmental effects. RESULTS: Rats prenatally treated with low-dose THC (LDTHC) generally had lower dark-cycle activity compared with control counterparts, but this altered activity was not observed at the higher dose of THC (HDTHC). In terms of open-field activity, THC doses displayed a general increase in locomotion. In addition, the LDTHC male rats in the ND showed significantly greater exploratory behavior. Prenatal THC had dose-dependent effects on maternal weight gain and birth weight. CONCLUSIONS: Overall, our findings indicate there are some activity-related and developmental effects of prenatal THC, which may be related to obesity risks later in life.

Vaporized nicotine in utero results in reduced birthweight, increased locomotion, and decreased voluntary exercise, dependent on sex and diet in offspring.

Rationale Clinical research has shown that prenatal exposure to nicotine may result in increased obesity risk later in life. Preclinical research has corroborated this finding, but few studies have investigated inhaled nicotine or the interaction with diet on obesity risk. Objective The aim of this study was to investigate the effects of prenatal nicotine exposure on both direct and indirect obesity measures, with both sex and diet as factors. Methods Pregnant rats were exposed to either vehicle or nicotine vapor (24 mg/mL or 59 mg/mL) throughout the entire gestational period. Offspring from each treatment group were given either a normal diet or a high fat diet starting at postnatal day 22. Caloric intake, body weight, spontaneous locomotion, sleep/wake activity, and voluntary exercise were measured throughout adolescence. Pregnancy weight gain and pup birthweights were collected to further measure developmental effects of prenatal nicotine exposure. Results Both maternal weight gain during pregnancy and pup weight at birth were decreased with prenatal nicotine exposure. Early adolescent males showed increased spontaneous activity in the open field following prenatal nicotine exposure compared to vehicle counterparts, particularly those given high-fat diet. Additionally, high dose nicotine prenatal treated males ran significantly less distance on the running wheel in late adolescence compared to vehicle counterparts, in the normal diet group only. Conclusion The results presented here show decreased birthweight, hyperactivity, and decreased voluntary exercise in adolescence following prenatal nicotine exposure in dose, sex, and diet dependent manners, which could lead to increased obesity risk in adulthood.

On Consistent Entropy-Regularized k-Means Clustering With Feature Weight Learning: Algorithm and Statistical Analyses.

Clusters in real data are often restricted to low-dimensional subspaces rather than the entire feature space. Recent approaches to circumvent this difficulty are often computationally inefficient and lack theoretical justification in terms of their large-sample behavior. This article deals with the problem by introducing an entropy incentive term to efficiently learn the feature importance within the framework of center-based clustering. A scalable block-coordinate descent algorithm, with closed-form updates, is incorporated to minimize the proposed objective function. We establish theoretical guarantees on our method by Vapnik-Chervonenkis (VC) theory to establish strong consistency along with uniform concentration bounds. The merits of our method are showcased through detailed experimental analysis on toy examples as well as real data clustering benchmarks.

Robust Principal Component Analysis: A Median of Means Approach.

Principal component analysis (PCA) is a fundamental tool for data visualization, denoising, and dimensionality reduction. It is widely popular in statistics, machine learning, computer vision, and related fields. However, PCA is well-known to fall prey to outliers and often fails to detect the true underlying low-dimensional structure within the dataset. Following the Median of Means (MoM) philosophy, recent supervised learning methods have shown great success in dealing with outlying observations without much compromise to their large sample theoretical properties. This article proposes a PCA procedure based on the MoM principle. Called the MoMPCA, the proposed method is not only computationally appealing but also achieves optimal convergence rates under minimal assumptions. In particular, we explore the nonasymptotic error bounds of the obtained solution via the aid of the Rademacher complexities while granting absolutely no assumption on the outlying observations. The derived concentration results are not dependent on the dimension because the analysis is conducted in a separable Hilbert space, and the results only depend on the fourth moment of the underlying distribution in the corresponding norm. The proposal's efficacy is also thoroughly showcased through simulations and real data applications.

Implicit Annealing in Kernel Spaces: A Strongly Consistent Clustering Approach.

Kernel k-means clustering is a powerful tool for unsupervised learning of non-linearly separable data. Its merits are thoroughly validated on a suite of simulated datasets and real data benchmarks that feature nonlinear and multi-view separation. Since the earliest attempts, researchers have noted that such algorithms often become trapped by local minima arising from the non-convexity of the underlying objective function. In this paper, we generalize recent results leveraging a general family of means to combat sub-optimal local solutions to the kernel and multi-kernel settings. Called Kernel Power k-Means, our algorithm uses majorization-minimization (MM) to better solve this non-convex problem. We show that the method implicitly performs annealing in kernel feature space while retaining efficient, closed-form updates. We rigorously characterize its convergence properties both from computational and statistical points of view. In particular, we characterize the large sample behavior of the proposed method by establishing strong consistency guarantees as well as finite-sample bounds on the excess risk of the estimates through modern tools in learning theory. The proposal's efficacy is demonstrated through an array of simulated and real data experiments.