A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
This paper identifies and estimates the label noise transition matrix without ground truth labels.
problem Learning with noisy labels and identifying the noise transition matrix.
method Building on Kruskal's identifiability results, the paper characterizes the identifiability of the label noise transition matrix for the generic case at the instance level.
result The necessity of multiple noisy labels in identifying the noise transition matrix for the generic case at the instance level.
We develop a topology data analysis-based method to detect early signs for critical transitions in financial data. From the time-series of multiple stock prices, we build time-dependent correlation networks, which exhibit topological structures. We compute the persistent homology associated to these structures in order…
In this paper we show that Cartan geometries can be studied via transitive Lie groupoids endowed with a special kind of vector-valued multiplicative 1-forms. This viewpoint leads us to a more general notion, that of Cartan bundle, which encompasses both Cartan geometries and G-structures.
Just like Atiyah Lie algebroids encode the infinitesimal symmetries of principal bundles, exact Courant algebroids are believed to encode the infinitesimal symmetries of S1-gerbes. At the same time, transitive Courant algebroids may be viewed as the higher analogue of Atiyah Lie algebroids, and the non-commutative a…
The goal of system identification is to learn about underlying physics dynamics behind the time-series data. To model the probabilistic and nonparametric dynamics model, Gaussian process (GP) have been widely used; GP can estimate the uncertainty of prediction and avoid over-fitting. Traditional GPSSMs, however, are ba…
The paper studies phase transitions in Information Bottleneck for representation learning.
problem Understanding the behavior of compression and prediction terms in IB objective.
method Studied phase transitions in IB objective using second-order calculus of variations and Fisher information matrix.
result IB phase transitions correspond to learning new classes and are related to maximum correlation between input and target orthogonal to the learned representation.
Deep conditional generative models are developed to simultaneously learn the temporal dependencies of multiple sequences. The model is designed by introducing a three-way weight tensor to capture the multiplicative interactions between side information and sequences. The proposed model builds on the Temporal Sigmoid Be…
Existing approaches to combine both additive and multiplicative neural units either use a fixed assignment of operations or require discrete optimization to determine what function a neuron should perform. However, this leads to an extensive increase in the computational complexity of the training procedure. We present…
Persistent entropy detects phase transitions in complex systems.
problem Detecting phase transitions in complex systems.
method Established a general theorem for persistent entropy to reliably detect phase transitions, introduced operational framework for finite-time computations.
result Persistent entropy exhibits an asymptotically non-vanishing gap across phases, robust numerical signatures across experiments.
Existing approaches to combine both additive and multiplicative neural units either use a fixed assignment of operations or require discrete optimization to determine what function a neuron should perform. This leads either to an inefficient distribution of computational resources or an extensive increase in the comput…
The principal aim of this work is the evidence on empirical way that catastrophic bifurcation breakdowns or transitions, proceeded by flickering phenomenon, are present on notoriously significant and unpredictable financial markets. Overall, in this work we developed various metrics associated with catastrophic bifurca…
Study on detecting hierarchical community structures in networks.
problem Detecting hierarchical community structures in networks.
method Analysis of planted hierarchies of partitions in networks, identifying additional detectability phases.
result There are additional phases in which the presence of multiple consistent partitions can either help or hinder detection of hierarchical structures.
We study learning latent models with multi-instance weak supervision.
problem Learning latent models with multi-instance weak supervision.
method Formulated as multi-instance Partial Label Learning (multi-instance PLL), proposed a necessary and sufficient condition for learnability, derived Rademacher-style error bounds.
result First theoretical study of multi-instance PLL with unknown transition function, aligns with empirical results but highlights scalability issues.
A critical decision point when training predictors using multiple studies is whether studies should be combined or treated separately. We compare two multi-study prediction approaches in the presence of potential heterogeneity in predictor-outcome relationships across datasets: 1) merging all of the datasets and traini…
We present a quantitative study of the markets and models evolution across the credit crunch crisis. In particular, we focus on the fixed income market and we analyze the most relevant empirical evidences regarding the divergences between Libor and OIS rates, the explosion of Basis Swaps spreads, and the diffusion of c…
This work improves transferability of rewards inferred from expert demonstrations.
problem Transferability of rewards inferred from expert demonstrations under limited access to the expert's policy.
method Proposed principal angles as a measure of similarity and dissimilarity between transition laws. Established sufficient conditions for transferability under limited access.
result Two key results on sufficient conditions for transferability to any and local changes in transition laws.
Long-term human motion can be represented as a series of motion modes---motion sequences that capture short-term temporal dynamics---with transitions between them. We leverage this structure and present a novel Motion Transformation Variational Auto-Encoders (MT-VAE) for learning motion sequence generation. Our model j…
We analyze an N+1-player game and the corresponding mean field game with state space {0,1}. The transition rate of j-th player is the sum of his control αj plus a minimum jumping rate η. Instead of working under monotonicity conditions, here we consider an anti-monotone running cost. We show that the mean …
In industrial systems, certain process variables that need to be monitored for detecting faults are often difficult or impossible to measure. Soft sensor techniques are widely used to estimate such difficult-to-measure process variables from easy-to-measure ones. Soft sensor modeling requires training datasets includin…