pwc-archive/papers-with-abstracts huggingface dataset:
PROMISE: Preconditioned Stochastic Optimization Methods by Incorporating Scalable Curvature Estimates
Authors: Zachary Frangella, Pratik Rathore, Shipu Zhao, Madeleine Udell
Date: 2023-09-05 00:00:00
Tasks: Stochastic Optimization

This paper introduces PROMISE ($\textbf{Pr}$econditioned Stochastic $\textbf{O}$ptimization $\textbf{M}$ethods by $\textbf{I}$ncorporating $\textbf{S}$calable Curvature $\textbf{E}$stimates), a suite of sketching-based preconditioned stochastic gradient algorithms for solving large-scale convex optimization problems arising in machine learning. PROMISE includes preconditioned versions of SVRG, SAGA, and Katyusha; each algorithm comes with a strong theoretical analysis and effective default hyperparameter values. In contrast, traditional stochastic gradient methods require careful hyperparameter tuning to succeed, and degrade in the presence of ill-conditioning, a ubiquitous phenomenon in machine learning. Empirically, we verify the superiority of the proposed algorithms by showing that, using default hyperparameter values, they outperform or match popular tuned stochastic gradient optimizers on a test bed of $51$ ridge and logistic regression problems assembled from benchmark machine learning repositories. On the theoretical side, this paper introduces the notion of quadratic regularity in order to establish linear convergence of all proposed methods even when the preconditioner is updated infrequently. The speed of linear convergence is determined by the quadratic regularity ratio, which often provides a tighter bound on the convergence rate compared to the condition number, both in theory and in practice, and explains the fast global linear convergence of the proposed methods.
Optimal Management of DC Pension Plan with Inflation Risk and Tail VaR Constraint
Authors: Hui Mi, Zuo Quan Xu, Dongfang Yang
Date: 2023-09-05 00:00:00
Tasks: Management

This paper investigates an optimal investment problem under the tail Value at Risk (tail VaR, also known as expected shortfall, conditional VaR, average VaR) and portfolio insurance constraints confronted by a defined-contribution pension member. The member's aim is to maximize the expected utility from the terminal wealth exceeding the minimum guarantee by investing his wealth in a cash bond, an inflation-linked bond and a stock. Due to the presence of the tail VaR constraint, the problem cannot be tackled by standard control tools. We apply the Lagrange method along with quantile optimization techniques to solve the problem. Through delicate analysis, the optimal investment output in closed-form and optimal investment strategy are derived. A numerical analysis is also provided to show how the constraints impact the optimal investment output and strategy.
Self-concordant Smoothing for Large-Scale Convex Composite Optimization
Authors: Adeyemi D. Adeoye, Alberto Bemporad
Date: 2023-09-04 00:00:00

We introduce a notion of self-concordant smoothing for minimizing the sum of two convex functions, one of which is smooth and the other may be nonsmooth. The key highlight of our approach is in a natural property of the resulting problem's structure which provides us with a variable-metric selection method and a step-length selection rule particularly suitable for proximal Newton-type algorithms. In addition, we efficiently handle specific structures promoted by the nonsmooth function, such as $\ell_1$-regularization and group-lasso penalties. We prove the convergence of two resulting algorithms: Prox-N-SCORE, a proximal Newton algorithm and Prox-GGN-SCORE, a proximal generalized Gauss-Newton algorithm. The Prox-GGN-SCORE algorithm highlights an important approximation procedure which helps to significantly reduce most of the computational overhead associated with the inverse Hessian. This approximation is essentially useful for overparameterized machine learning models and in the mini-batch settings. Numerical examples on both synthetic and real datasets demonstrate the efficiency of our approach and its superiority over existing approaches. A Julia package implementing the proposed algorithms is available at https://github.com/adeyemiadeoye/SelfConcordantSmoothOptimization.jl.
On Penalty Methods for Nonconvex Bilevel Optimization and First-Order Stochastic Approximation
Authors: Jeongyeol Kwon, Dohyun Kwon, Stephen Wright, Robert Nowak
Date: 2023-09-04 00:00:00
Tasks: Bilevel Optimization

In this work, we study first-order algorithms for solving Bilevel Optimization (BO) where the objective functions are smooth but possibly nonconvex in both levels and the variables are restricted to closed convex sets. As a first step, we study the landscape of BO through the lens of penalty methods, in which the upper- and lower-level objectives are combined in a weighted sum with penalty parameter $\sigma > 0$. In particular, we establish a strong connection between the penalty function and the hyper-objective by explicitly characterizing the conditions under which the values and derivatives of the two must be $O(\sigma)$-close. A by-product of our analysis is the explicit formula for the gradient of hyper-objective when the lower-level problem has multiple solutions under minimal conditions, which could be of independent interest. Next, viewing the penalty formulation as $O(\sigma)$-approximation of the original BO, we propose first-order algorithms that find an $\epsilon$-stationary solution by optimizing the penalty formulation with $\sigma = O(\epsilon)$. When the perturbed lower-level problem uniformly satisfies the small-error proximal error-bound (EB) condition, we propose a first-order algorithm that converges to an $\epsilon$-stationary point of the penalty function, using in total $O(\epsilon^{-3})$ and $O(\epsilon^{-7})$ accesses to first-order (stochastic) gradient oracles when the oracle is deterministic and oracles are noisy, respectively. Under an additional assumption on stochastic oracles, we show that the algorithm can be implemented in a fully {\it single-loop} manner, i.e., with $O(1)$ samples per iteration, and achieves the improved oracle-complexity of $O(\epsilon^{-3})$ and $O(\epsilon^{-5})$, respectively.
Modified Step Size for Enhanced Stochastic Gradient Descent: Convergence and Experiments
Authors: M. Soheil Shamaee, S. Fathi Hafshejani
Date: 2023-09-03 00:00:00
Tasks: image-classification, Image Classification

This paper introduces a novel approach to enhance the performance of the stochastic gradient descent (SGD) algorithm by incorporating a modified decay step size based on $\frac{1}{\sqrt{t}}$. The proposed step size integrates a logarithmic term, leading to the selection of smaller values in the final iterations. Our analysis establishes a convergence rate of $O(\frac{\ln T}{\sqrt{T}})$ for smooth non-convex functions without the Polyak-{\L}ojasiewicz condition. To evaluate the effectiveness of our approach, we conducted numerical experiments on image classification tasks using the FashionMNIST, and CIFAR10 datasets, and the results demonstrate significant improvements in accuracy, with enhancements of $0.5\%$ and $1.4\%$ observed, respectively, compared to the traditional $\frac{1}{\sqrt{t}}$ step size. The source code can be found at \\\url{https://github.com/Shamaeem/LNSQRTStepSize}.
Single-cell mutational burden distributions in birth-death processes
Authors: Christo Morison, Dudley Stark, Weini Huang
Date: 2023-09-12 00:00:00

Genetic mutations are footprints of tumour growth. While mutation data in bulk samples has been used to infer evolutionary parameters hard to measure in vivo, the advent of single-cell data has led to strong interest in the mutational burden distribution (MBD) among tumour cells. We introduce dynamical matrices and recurrence relations to integrate this single-cell MBD with known statistics, and derive new analytical expressions. Surprisingly, we find that the shape of the MBD is driven by cell lineage-level stochasticity rather than by the distribution of mutations in each cell division.
Thiele's PIDE for unit-linked policies in the Heston-Hawkes stochastic volatility model
Authors: David R. Baños, Salvador Ortiz-Latorre, Oriol Zamora Font
Date: 2023-09-07 00:00:00
Tasks: Clustering

The main purpose of the paper is to derive Thiele's differential equation for unit-linked policies in the Heston-Hawkes stochastic volatility model introduced in arXiv:2210.15343. This model is an extension of the well-known Heston model that incorporates the volatility clustering feature by adding a compound Hawkes process in the volatility. Since the model is arbitrage-free, pricing unit-linked policies via the equivalence principle under a risk neutral probability measure is possible. Studying the moments of the variance and certain stochastic exponentials, a suitable family of risk neutral probability measures is found. The established and practical method to compute reserves in life insurance is by solving Thiele's equation, which is crucial to guarantee the solvency of the insurance company.
Modelling gene content across a phylogeny to determine when genes become associated
Authors: Jiahao Diao, Malgorzata M. O'Reilly, Barbara R. Holland
Date: 2023-09-06 00:00:00

In this work, we develop a stochastic model of gene gain and loss with the aim of inferring when (if at all) in evolutionary history and association between two genes arises. The data we consider is a species tree along with information on the presence or absence of two genes in each of the species. The biological motivation for our model is that if two genes are involved in the same biochemical pathway, i.e. they are both required for some function, then the rate of gain or loss of one gene in the pathway should depend upon the presence or absence of the other gene in the pathway. However, if the two genes are not functionally linked, then the rate of gain or loss of one gene should be independent of the state of another gene. We simulate data under this model to determine under what conditions a shift from the independent rates class to the dependent rates class can be detected. For example, how large a tree is required and how large a shift in the rates is needed before Akaike information criterion (AIC) supports a model with two rate classes over a simpler model with just one rate class? If a model with two rate classes is preferred, can it correctly detect where on the evolutionary tree the shift occurred?
Stochastic niche-based models for the evolution of species
Authors: Albert Ch. Soewongsono, Barbara R. Holland, Malgorzata M. O'Reilly
Date: 2023-09-06 00:00:00

There have been many studies to examine whether one trait is correlated with another trait across a group of present-day species (for example, do species with larger brains tend to have longer gestation times. Since the introduction of the phylogenetic comparative method some authors have argued that it is necessary to have a biologically realistic model to generate evolutionary trees that incorporates information about the ecological niche occupied by species. Price presented a simple model along these lines in 1997. He defined a two-dimensional niche space formed by two continuous-valued traits, in which new niches arise with trait values drawn from a bivariate normal distribution. When a new niche arises, it is occupied by a descendant species of whichever current species is closest in ecological niche space. In sequence, more species are then evolved from already-existing species to which they are ecologically closest. Here we explore ways of extending Price's adaptive radiation model. One extension is to increase the dimensionality of the niche space by considering more than two continuous traits. A second extension is to allow both extinction of species (which may leave unoccupied niches) and removal of niches (which causes species occupying them to go extinct). To model this problem, we consider a continuous-time stochastic process which implicitly defines a phylogeny. To explore if trees generated under such a model (or under different parametrizations of the model) are realistic we can compute a variety of summary statistics that can be compared to those of empirically observed phylogenies. For example, there are existing statistics that aim to measure: tree balance, the relative rate of diversification, and phylogenetic signal of traits.
A Comparative Evaluation of FedAvg and Per-FedAvg Algorithms for Dirichlet Distributed Heterogeneous Data
Authors: Hamza Reguieg, Mohammed El Hanjri, Mohamed El Kamili, Abdellatif Kobbane
Date: 2023-09-03 00:00:00
Tasks: Federated Learning

In this paper, we investigate Federated Learning (FL), a paradigm of machine learning that allows for decentralized model training on devices without sharing raw data, there by preserving data privacy. In particular, we compare two strategies within this paradigm: Federated Averaging (FedAvg) and Personalized Federated Averaging (Per-FedAvg), focusing on their performance with Non-Identically and Independently Distributed (Non-IID) data. Our analysis shows that the level of data heterogeneity, modeled using a Dirichlet distribution, significantly affects the performance of both strategies, with Per-FedAvg showing superior robustness in conditions of high heterogeneity. Our results provide insights into the development of more effective and efficient machine learning strategies in a decentralized setting.
From constant to rough: A survey of continuous volatility modeling
Authors: Giulia Di Nunno, Kęstutis Kubilius, Yuliya Mishura, Anton Yurchenko-Tytarenko
Date: 2023-09-02 00:00:00
Tasks: Survey

In this paper, we present a comprehensive survey of continuous stochastic volatility models, discussing their historical development and the key stylized facts that have driven the field. Special attention is dedicated to fractional and rough methods: we outline the motivation behind them and characterize some landmark models. In addition, we briefly touch the problem of VIX modeling and recent advances in the SPX-VIX joint calibration puzzle.
Ein neuer Ansatz zur Frequenzmodellierung im Versicherungswesen (A new Approach to frequency modeling in risk theory)
Authors: Dietmar Pfeifer
Date: 2023-08-23 00:00:00

The collective risk model differentiates usually between claims frequencies (and their distribution) and claim sizes (and their distribution). For the claims frequencies typically classical discrete distributions are considered, such as Binomial-, Negative binomial- or Poisson distributions. Since these distributions sometimes do not really fit to the data we propose a different approach here for claim frequencies via random proportions of the number of insurance contracts. This approach also allows for a statistical goodness-of-fit test via quantile-quantile-plots and can likewise be applied to the modelling of claim size distributions.
ChemSpaceAL: An Efficient Active Learning Methodology Applied to Protein-Specific Molecular Generation
Authors: Gregory W. Kyro, Anton Morgunov, Rafael I. Brent, Victor S. Batista
Date: 2023-09-11 00:00:00
Tasks: Active Learning, Drug Discovery

The incredible capabilities of generative artificial intelligence models have inevitably led to their application in the domain of drug discovery. Within this domain, the vastness of chemical space motivates the development of more efficient methods for identifying regions with molecules that exhibit desired characteristics. In this work, we present a computationally efficient active learning methodology that requires evaluation of only a subset of the generated data in the constructed sample space to successfully align a generative model with respect to a specified objective. We demonstrate the applicability of this methodology to targeted molecular generation by fine-tuning a GPT-based molecular generator toward a protein with FDA-approved small-molecule inhibitors, c-Abl kinase. Remarkably, the model learns to generate molecules similar to the inhibitors without prior knowledge of their existence, and even reproduces two of them exactly. We also show that the methodology is effective for a protein without any commercially available small-molecule inhibitors, the HNH domain of the CRISPR-associated protein 9 (Cas9) enzyme. We believe that the inherent generality of this method ensures that it will remain applicable as the exciting field of in silico molecular generation evolves. To facilitate implementation and reproducibility, we have made all of our software available through the open-source ChemSpaceAL Python package.
Navigating Homogeneous Paths through Amyloidogenic and Non-Amyloidogenic Hexapeptides
Authors: Laszlo Keresztes, Evelin Szogi, Balint Varga, Viktor Farkas, Andras Perczel, Vince Grolmusz
Date: 2023-09-07 00:00:00

Hexapeptides are increasingly applied as model systems for studying the amyloidogenecity properties of oligo- and polypeptides. It is possible to construct 64 million different hexapeptides from the twenty proteinogenic amino acid residues. Today's experimental amyloid databases contain only a fraction of these annotated hexapeptides. For labeling all the possible hexapeptides as "amyloidogenic" or "non-amyloidogenic" there exist several computational predictors with good accuracies. It may be of interest to define and study a simple graph structure on the 64 million hexapeptides as nodes when two hexapeptides are connected by an edge if they differ by only a single residue. For example, in this graph, HIKKLM is connected to AIKKLM, or HIKKNM, or HIKKLC, but it is not connected with an edge to VVKKLM or HIKNPM. In the present contribution, we consider our previously published artificial intelligence-based tool, the Budapest Amyloid Predictor (BAP for short), and demonstrate a spectacular property of this predictor in the graph defined above. We show that for any two hexapeptides predicted to be "amyloidogenic" by the BAP predictor, there exists an easily constructible path of length at most 6 that passes through neighboring hexapeptides all predicted to be "amyloidogenic" by BAP. For example, the predicted amyloidogenic ILVWIW and FWLCYL hexapeptides can be connected through the length-6 path ILVWIW-IWVWIW-IWVCIW-IWVCIL-FWVCIL-FWLCIL-FWLCYL in such a way that the neighbors differ in exactly one residue, and all hexapeptides on the path are predicted to be amyloidogenic by BAP. The symmetric statement also holds for non-amyloidogenic hexapeptides. It is noted that the mentioned property of the Budapest Amyloid Predictor \url{https://pitgroup.org/bap} is not proprietary; it is also true for any linear Support Vector Machine (SVM)-based predictors.
NLRP3 monomer Functional Dynamics: from the Effects of Allosteric Binding to Implications for Drug Design
Authors: Emanuele Casali, Stefano A. Serapian, Eleonora Gianquinto, Matteo Castelli, Massimo Bertinaria, Francesca Spyrakis, Giorgio Colombo
Date: 2023-09-07 00:00:00
Tasks: Drug Design

The protein NLRP3 and its complexes are associated with an array of inflammatory pathologies, among which neurodegenerative, autoimmune, and metabolic diseases. Targeting the NLRP3 inflammasome represents a promising strategy for easing the symptoms of pathologic neuroinflammation. When the inflammasome is activated, NLRP3 undergoes a conformational change triggering the production of pro-inflammatory cytokines IL-1\beta and IL-18, as well as cell death by pyroptosis. NLRP3 nucleotide-binding and oligomerization (NACHT) domain plays a crucial role in this function by binding and hydrolysing ATP and is primarily responsible, together with conformational transitions involving the PYD domain, for the complex-assembly process. Allosteric ligands proved able to induce NLRP3 inhibition. Herein, we examine the origins of allosteric inhibition of NLRP3. Through the use of molecular dynamics (MD) simulations and advanced analysis methods, we provide molecular-level insights into how allosteric binding affects protein structure and dynamics, remodelling of the conformational ensembles populated by the protein, with key reverberations on how NLRP3 is preorganized for assembly and ultimately function. The data are used to develop a Machine Learning model to define the protein as Active or Inactive, only based on the analysis of its internal dynamics. We propose this model as a novel tool to select allosteric ligands.
Enumeration of saturated and unsaturated substituted N-heterocycles
Authors: Stefan Schuster, Tatjana Malycheva
Date: 2023-09-05 00:00:00

Mathematical and computational approaches in chemistry and biochemistry fill a gap in respect to the analysis of the physicochemical features of compounds and their functionality and provide an overview of known as well as yet unknown, but hypothetically possible structures. Nitrogen-containing heterocycles such as aziridine, azetidine and pyrrolidine bear a high potential in pharmacology, biotechnology and synthetic biology. Here, we present a mathematical enumeration procedure for all possible azaheterocycles with at least one substituent depending on the number of atoms in the ring, in the sense of saturated and unsaturated congeners. One subgroup belonging to that substance class is constituted by ring-shaped amino acids with a secondary amino group, such as proline. A recursion formula is derived, which results in a modified Lucas number series. Moreover, an explicit formula for determining the number of such substances based on the Golden Ratio is given and a second one, based on binomial coefficients, is newly derived. This enumeration is a helpful tool for construction or complementation of virtual compound databases and for computer-assisted chemical synthesis route planning.
DCAlign v1.0: Aligning biological sequences using co-evolution models and informed priors
Authors: Anna Paola Muntoni, Andrea Pagnani
Date: 2023-09-04 00:00:00

DCAlign is a new alignment method able to cope with the conservation and the co-evolution signals that characterize the columns of multiple sequence alignments of homologous sequences. However, the pre-processing steps required to align a candidate sequence are computationally demanding. We show in v1.0 how to dramatically reduce the overall computing time by including an empirical prior over an informative set of variables mirroring the presence of insertions and deletions.
A dynamic fluid landscape mediates the spread of bacteria
Authors: Divakar Badal, Aloke Kumar, Varsha Singh, Danny Raj M
Date: 2023-09-11 00:00:00

Microbial interactions regulate their spread and survival in competitive environments. It is not clear if the physical parameters of the environment regulate the outcome of these interactions. In this work, we show that the opportunistic pathogen Pseudomonas aeruginosa occupies a larger area on the substratum in the presence of yeast such as Cryptococcus neoformans , than without it. At the microscopic level, bacterial cells show an enhanced activity in the vicinity of yeast cells. We observe this behaviour even when the live yeast cells are replaced with heat-killed cells or with spherical glass beads of similar morphology, which suggests that the observed behaviour is not specific to the biology of microbes. Upon careful investigation, we find that a fluid pool is formed around yeast cells which facilitates the swimming of the flagellated P. aeruginosa , causing their enhanced motility. Using mathematical modeling we demonstrate how this local enhancement of bacterial motility leads to the enhanced spread observed at the level of the plate. We find that the dynamics of the fluid landscape around the bacteria, mediated by the growing yeast lawn, affects the spreading. For instance, when the yeast lawn grows faster, a bacterial colony prefers a lower initial loading of yeast cells for optimum enhancement in the spread. We confirm our predictions using Candida albicans and C. neoformans, at different initial compositions. In summary, our work shows the importance of considering the dynamically changing physical environment while studying bacterial motility in complex environments.