Andrei Lyashenko’s Post

#Industrial #AAD Algorithmic Automatic Differentiation (#AAD) is a technique that allows you to compute the #sensitivities of any function 𝑓with 𝑛 variables (𝑥1,𝑥2,…,𝑥𝑛) at a #computation #cost of just 4 calls of the function 𝑓 independent of 𝑛, which is for me always like #magic 🧙♂️ 🧙♂️ 🧙♂️ ! 🈸 https://lnkd.in/dBAVBaS6 📘 Applying AAD to #local #volatility vega KT is a remarkable demonstration of this theory, bringing both speed and quality improvements at an industrial level. 🈸 https://lnkd.in/dKX9mnrs 📄 🈸 https://lnkd.in/djika-pY 📄 This technique is one of the key pillars for Neural Network development, particularly in the area of backpropagation. AAD can also #improve pricing, not just sensitivity calculations, by interpreting prices as sensitivities using perturbation techniques. 🈸 https://lnkd.in/drkb_n7X 📄 🈸 https://lnkd.in/eDwNt3B8 📄 🈸 https://lnkd.in/dAg_tNAN 📄 🈸 https://lnkd.in/dGfrXzb3 📄 In this final work, we adopt a #partial approach, drawing on Pontryagin's key idea that calculating sensitivities is essentially finding the Jacobian and matrix multiplication. By organizing these calculations, we achieve the necessary optimization in the very challenging LSV set up. In this paper, we conduct a #partial #backward #calculation of AAD, avoiding the challenging part of calibration in the LSV model. I am thrilled to share with my network this #collaborative work from my previous job with my esteemed colleagues Abdessamad Sahnoun, leopold FONGANG, Marouen Messaoud, Mahi Rida, William LEDUC, which has finally been published 🈸 https://lnkd.in/dt7kXH2N 📘 🈸 https://lnkd.in/dhnt2b-7 📄 This opens up new #industrial methods for implementing AAD when the calibration is challenging. The same technique can be applied to nonlinear dividends and local correlation to cite some important examples, not only to compute price impacts but also sensitivities. Many thanks, Adil

This paper demonstrates the use of the Black-Litterman (BL) portfolio allocation model by integrating Bayesian methods and data fusion techniques to handle multiple, often uncertain investor views. The authors address scenarios where machine learning (ML) models generate diverse predictions about asset returns, leading to complex, sometimes conflicting perspectives. By applying Bayesian inference, the BL model updates beliefs about expected returns based on subjective views, optimizing asset weights within a mean-variance framework. To further enhance robustness, the paper explores consistency-based information fusion methods, such as Precision-Weighted and Covariance Intersection (CI), enabling the model to synthesize multiple ML-derived forecasts into a cohesive, uncertainty-weighted allocation strategy. This approach demonstrates a way to blend BL with advanced data fusion to potentially improve portfolio performance by reconciling diverse, uncertain views on asset returns.

Bayes' theorem is a mathematical formula for determining conditional probability of an event. Learn how to calculate Bayes' theorem and see examples.

Reproducing Kernel Hilbert Spaces and Mercer's Theorem: Mercer's Theorem and Reproducing Kernel Hilbert Spaces (RKHSs) are important concepts of Functional Analysis, related to each other, and with applications in different fields. Before presenting them, it is necessary to define a Mercer kernel, which is the link between both concepts. Let (X,d) be a metric space. The function K:XxX--->R is a Mercer kernel (Mercer (1909)) if it is continuous, symmetric and positive semidefinite. If we consider the closure of the set of linear combinations of a Mercer kernel, it is possible to define over it an inner product that makes it a Hilbert space, known as the Reproducing Kernel Hilbert Space (RKHS) associated with the kernel K. Now suppose that X is compact and mu is a finite Borel measure on (X,d) and define the operator L_K, determined by the first two formulas below, where K is a Mercer kernel. The operator L_K is compact, self-adjoint and positive. Therefore, there exists an orthonormal basis {phi_i} of L^2(X,mu) consisting of eigenfunctions of L_K. Their corresponding eigenvalues, {lambda_k} are non-negative, bounded and with lim lambda_k=0 if they are infinitely many. Furthermore, the set {sqrt(lambda_k)*phi_k} is an orthonormal basis of the RKHS associated with K (see, for example, Cucker et al. (2007) for the proof of these results). Mercer's Theorem states that, if mu is non-degenerate, the kernel K can be expressed as in the last formula, with absolute convergence (for each (x,y) belonging to XxX) and uniform convergence (over XxX). See first comment for some applications in Machine Learning and Finance. References: - Bueno-Guerrero, Moreno and Navas (2016): "The Stochastic String Model as a Unifying Theory of the Term Structure of Interest Rates", Physica A, 461, 217-237. - Bueno-Guerrero, Moreno and Navas (2017): "Malliavin Calculus for Stochastic Strings with Applications to Barrier Options and Optimal Portfolios", SSRN (https://lnkd.in/dyqWbiFy). - Cucker and Xuan Zhou (2007): "Learning Theory: An Approximation Theory Viewpoint", Cambridge University Press. - Evgeniou, Pontil and Poggio (2000): "Regularization Networks and Support Vector Machines", Advances in Computational Mathematics, 13, 1–50. - Mercer (1909): "Functions of Positive and Negative Type and their connection with the Theory of Integral Equations", Philosophical Transactions of the Royal Society of London, 209, 415-446. #finance #mathematics #markets #machinelearning

Usually, I use interpretability and explainability exchangeably, but I've found a distinction I like more: Explainability requires interpretability but additionally depends on the context and the "user" of the explanation. It's more than interpretability. This distinction is based on the paper "Explainable Machine Learning for Scientific Insights and Discoveries" by Roscher et. al. Others make a different distinction: Interpretable for "inherently interpretable" models and explainability for post-hoc methods. But I'm not a fan, for two reasons: 1) lines are blurry between the two categories, think of marginal effects for logistic regression. Or if you compute SHAP values for GAMs, they are the same as the feature effects in the GAM (with a constant shift). 2) to me the term explainability sounds like having a higher bar than interpretability. For example, permutation feature importance would be counted as an "explainability method", but model interpretation sounds much more nuanced.

What happens when you want to optimize a plethora of different objectives instead of just only the prediction error or prediction time of machine learning models with respect to their hyperparameter values? You have what is known as a many objective problem. You can use lots of techniques coming from the many objective optimization field also in Bayesian optimization. Discover some early research in this topic here and DM me if you are interested on this field. https://lnkd.in/diQucnjC

#SUERFpolicybrief “Machine learning applied to active fixed-income portfolio management: a Lasso logit approach” by Mercedes de Luis López, Emilio Rodriguez, CFA and Diego Torres (Banco de España) This policy brief note is based on a working paper that investigates the performance of machine learning algorithms, particularly Lasso Logit Regression, in actively managed high-grade bond portfolios. It emphasizes the superior performance of ensemble algorithms and underscores the significance of the proposed signal translation approach. Notably, a noteworthy portion of alpha generation stems from the identification of 'extreme' movements, while it also highlights the presence of time-dependency and instability in selected financial and economic variables. https://lnkd.in/dcrEGGPm #MachineLearning #ProbabilisticOrClassificationModels #LassoLogitRegressions #ActiveFixedIncomeManagement #AbsoluteExcessReturn #SharpeRatios #DurationManagement

Bayes' theorem is a mathematical formula for determining conditional probability of an event. Learn how to calculate Bayes' theorem and see examples.

*** Markov Model: Explained *** ~ In probability theory, a Markov model is a stochastic model used to model pseudo-randomly changing systems. It is assumed that future states depend only on the current state, not on the events that occurred before it (that is, it assumes the Markov property). ~ Generally, this assumption enables reasoning and computation with the model that would otherwise be intractable. For this reason, a given model should exhibit the Markov property in predictive modeling and probabilistic forecasting. ~ There are three standard Markov models used in different situations, depending on whether every sequential state is observable or not and whether the system is to be adjusted based on observations made: ~ The simplest Markov model is the Markov chain. It models the state of a system with a random variable that changes through time. In this context, the Markov property indicates that the distribution for this variable depends only on the distribution of a previous state. ~ An example of a Markov chain is the Markov chain Monte Carlo, which uses the Markov property to prove that a particular method for performing a random walk will sample from the joint distribution. ~ A hidden Markov model is a Markov chain where the state is only partially or noisily observable. In other words, observations are related to the system's state but are typically insufficient to determine the state precisely. ~ Several well-known algorithms for hidden Markov models exist. For example, given a sequence of observations, the Viterbi algorithm will compute the most likely corresponding sequence of states, the forward algorithm will calculate the probability of the sequence of observations, and the Baum–Welch algorithm will estimate the starting probabilities, the transition function, and the observation function of a hidden Markov model. ~ One everyday use is for speech recognition, where the observed data is the speech audio waveform and the hidden state is the spoken text. In this example, the Viterbi algorithm finds the most likely sequence of spoken words given the speech audio. ~ Markov chains have been used as a forecasting method for several topics, for example, price trends, wind power, and solar irradiance. ~ The Markov-chain forecasting models utilize various settings, from discretizing the time series to hidden Markov models combined with wavelets and the Markov-chain mixture distribution model (MCM). --- B. Noted

Excited to share my paper " Harnessing Machine Learning for Efficient Partial Discharge Detection in High Voltage Systems". In high-voltage systems, partial discharge (PD) must be detected and controlled in order to guarantee operational safety and dependability. Conventional techniques include drawbacks such noise interference, temporal localization, and dependence on small datasets, which might result in errors. Through the use of data-driven methodologies, machine learning (ML) provides a promising way to improve the scalability, efficiency, and accuracy of PD detection. Machine learning models (ML) facilitate real-time monitoring, predictive maintenance, and early defect identification by automatically deriving complicated patterns from high-dimensional data. This reduces downtime and averts catastrophic failures.