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We analyze the prediction error of principal component regression (PCR) and prove high probability bounds for the corresponding squared risk conditional on the design. Our first main result shows that PCR performs comparably to the oracle…

The recent banking crisis has again emphasized the importance of understanding and mitigating systemic risk in financial networks. In this paper, we study a market-driven approach to rescue a bank in distress based on the idea of claims…

We propose a multiple imputation method based on principal component analysis (PCA) to deal with incomplete continuous data. To reflect the uncertainty of the parameters from one imputation to the next, we use a Bayesian treatment of the…

The 2008 financial crisis illustrated the need for a thorough, functional understanding of systemic risk in strongly interconnected financial structures. Dynamic processes on complex networks being intrinsically difficult, most recent…

Principal Component Analysis (PCA) is a transform for finding the principal components (PCs) that represent features of random data. PCA also provides a reconstruction of the PCs to the original data. We consider an extension of PCA which…

Principal Component Analysis (PCA) is the most widely used tool for linear dimensionality reduction and clustering. Still it is highly sensitive to outliers and does not scale well with respect to the number of data samples. Robust PCA…

Principal component analysis (PCA) is a well-established method commonly used to explore and visualise data. A classical PCA model is the fixed effect model where data are generated as a fixed structure of low rank corrupted by noise. Under…

The principal component analysis (PCA) is a staple statistical and unsupervised machine learning technique in finance. The application of PCA in a financial setting is associated with several technical difficulties, such as numerical…

We introduce a class of copulas that we call Principal Component Copulas (PCCs). This class combines the strong points of copula-based techniques with principal component analysis (PCA), which results in flexibility when modelling tail…

Principal component analysis (PCA) is a classical method for dimensionality reduction based on extracting the dominant eigenvectors of the sample covariance matrix. However, PCA is well known to behave poorly in the ``large $p$, small $n$''…

As economic entities become increasingly interconnected, a shock in a financial network can provoke significant cascading failures throughout the system. To study the systemic risk of financial systems, we create a bi-partite banking…

In this paper, a new method is proposed for sparse PCA based on the recursive divide-and-conquer methodology. The main idea is to separate the original sparse PCA problem into a series of much simpler sub-problems, each having a closed-form…

We explore a model of the interaction between banks and outside investors in which the ability of banks to issue inside money (short-term liabilities believed to be convertible into currency at par) can generate a collapse in asset prices…

The fragility of financial systems was starkly demonstrated in early 2023 through a cascade of major bank failures in the United States, including the second, third, and fourth largest collapses in the US history. The highly interdependent…

Operational risk is the risk relative to monetary losses caused by failures of bank internal processes due to heterogeneous causes. A dynamical model including both spontaneous generation of losses and generation via interactions between…

Large Language Models (LLMs) have demonstrated remarkable reasoning abilities on complex problems using long Chain-of-Thought (CoT) reasoning. However, they often suffer from overthinking, meaning generating unnecessarily lengthy reasoning…

A novel procedure is presented for the objective comparison and evaluation of a bank's decision rules in optimising the timing of loan recovery. This procedure is based on finding a delinquency threshold at which the financial loss of a…

Principal component analysis (PCA) aims at estimating the direction of maximal variability of a high-dimensional dataset. A natural question is: does this task become easier, and estimation more accurate, when we exploit additional…

Classical machine learning algorithms often face scalability bottlenecks when they are applied to large-scale data. Such algorithms were designed to work with small data that is assumed to fit in the memory of one machine. In this report,…

Principal Component Analysis (PCA) is one of the most important unsupervised methods to handle high-dimensional data. However, due to the high computational complexity of its eigen decomposition solution, it hard to apply PCA to the…