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.
Fixed-parameter tractability of private synthetic data generation
Many polynomial invariants of knots and links, including the Jones and HOMFLY-PT polynomials, are widely used in practice but #P-hard to compute. It was shown by Makowsky in 2001 that computing the Jones polynomial is fixed-parameter tractable in the treewidth of the link diagram, but the parameterised complexity of th…
New algorithm speeds up knot polynomial calculations.
To enumerate 3-manifold triangulations with a given property, one typically begins with a set of potential face pairing graphs (also known as dual 1-skeletons), and then attempts to flesh each graph out into full triangulations using an exponential-time enumeration. However, asymptotically most graphs do not result in …
In graph theory, Courcelle's theorem essentially states that, if an algorithmic problem can be formulated in monadic second-order logic, then it can be solved in linear time for graphs of bounded treewidth. We prove such a metatheorem for a general class of triangulations of arbitrary fixed dimension d, including all t…
Algorithm computes quantum invariants efficiently using carving-width.
Paper introduces TtT, market-implied transition time, from greenium term structure.
Study on teaching complexity in graphs, proving hardness and tractability.
Optimal Morse matchings reveal essential structures of cell complexes which lead to powerful tools to study discrete geometrical objects, in particular discrete 3-manifolds. However, such matchings are known to be NP-hard to compute on 3-manifolds, through a reduction to the erasability problem. Here, we refine the stu…
Algorithm efficiently learns deep ReLU networks with polynomial runtime in depth and parameters.
Study shortest non-separating curves on non-orientable surfaces, proving NP-hardness and tractability.
Training neural networks is hard in fixed dimensions.
EPMF factorizes matrices by adjusting their entries to match a specified power.
FNFs model parameter-dependent densities by combining a fixed flow with a polynomial parameter-dependent transformation.
Tractable model explains market dynamics using Langevin and SUSY QM.
Algorithm calculates quantum invariants of 3-manifolds with polynomial time complexity.
There are many fundamental algorithmic problems on triangulated 3-manifolds whose complexities are unknown. Here we study the problem of finding a taut angle structure on a 3-manifold triangulation, whose existence has implications for both the geometry and combinatorics of the triangulation. We prove that detecting ta…
Complex phenomena in engineering and the sciences are often modeled with computationally intensive feed-forward simulations for which a tractable analytic likelihood does not exist. In these cases, it is sometimes necessary to estimate an approximate likelihood or fit a fast emulator model for efficient statistical inf…
The Turaev-Viro invariants are a powerful family of topological invariants for distinguishing between different 3-manifolds. They are invaluable for mathematical software, but current algorithms to compute them require exponential time. The invariants are parameterised by an integer . We resolve the question …
In this paper we present decomposable priors, a family of priors over structure and parameters of tree belief nets for which Bayesian learning with complete observations is tractable, in the sense that the posterior is also decomposable and can be completely determined analytically in polynomial time. This follows from…
Bayesian model selection optimizes data augmentation for improved machine learning robustness.
Proposes methods to accurately learn manifolds and their distributions.
In this article, we introduce a fixed parameter tractable algorithm for computing the Turaev-Viro invariants TV(4,q), using the dimension of the first homology group of the manifold as parameter. This is, to our knowledge, the first parameterised algorithm in computational 3-manifold topology using a topological parame…
In this paper, we relax the power parameter of instantaneous variance and develop a new stochastic volatility plus jumps model that generalize the Heston model and 3/2 model as special cases. This model has two distinctive features. First, we do not restrict the new parameter, letting the data speak as to its direction…
Proposes a new model to better handle correlation risk in credit risk calculations.
The discrete-time multifactor Vasiček model is a tractable Gaussian spot rate model. Typically, two- or three-factor versions allow one to capture the dependence structure between yields with different times to maturity in an appropriate way. In practice, re-calibration of the model to the prevailing market conditions …
The Neural Autoregressive Distribution Estimator (NADE) and its real-valued version RNADE are competitive density models of multidimensional data across a variety of domains. These models use a fixed, arbitrary ordering of the data dimensions. One can easily condition on variables at the beginning of the ordering, and …
The analytical tractability of affine (short rate) models, such as the Vasicek and the Cox-Ingersoll-Ross models, has made them a popular choice for modelling the dynamics of interest rates. However, in order to account properly for the dynamics of real data, these models need to exhibit time-dependent or even stochast…
Optimal crypto asset routing with CFMMs, including fixed costs.
RTRL optimizes long sequences without truncation, converging to loss minima.
Simplifies inference for simulators with or without tractable likelihoods.
Paper shows how to infer hidden states in neural networks analytically.
Develops a computationally tractable differentially private mean estimator called the balloon mean.
A hybrid framework for American option pricing under time-varying rough volatility.
A new model explains relative spreads between economies using dynamic Nelson-Siegel and functional regression.
The paper explores algorithms to transform 3-manifold triangulations while controlling sparsity.
Inference is typically intractable in high-treewidth undirected graphical models, making maximum likelihood learning a challenge. One way to overcome this is to restrict parameters to a tractable set, most typically the set of tree-structured parameters. This paper explores an alternative notion of a tractable set, nam…
MLP residual networks implement a selective coarse-graining procedure governed by the spectral structure of the input distribution.
We introduce RNADE, a new model for joint density estimation of real-valued vectors. Our model calculates the density of a datapoint as the product of one-dimensional conditionals modeled using mixture density networks with shared parameters. RNADE learns a distributed representation of the data, while having a tractab…
In this paper we develop a tractable structural model with analytical default probabilities depending on some dynamics parameters, and we show how to calibrate the model using a chosen number of Credit Default Swap (CDS) market quotes. We essentially show how to use structural models with a calibration capability that …
Develops 2-categorical methods for multi-parameter persistence.
Neural networks struggle with learning fixed parities.
Proposes second-order Esscher transform for Lévy models in financial markets.
Affine term structure models have gained significant attention in the finance literature, mainly due to their analytical tractability and statistical flexibility. The aim of this article is to present both theoretical foundations as well as empirical aspects of the affine model class. Starting from the original one-fac…
New algorithm for weighted low rank approximation with provable guarantees.
New method for initializing low-rank neural networks improves performance.
Motivated by fixed-parameter tractable (FPT) problems in computational topology, we consider the treewidth of a compact, connected 3-manifold defined by \[ \operatorname{tw}(M) = \min\{\operatorname{tw}(Γ(\mathcal{T})):\mathcal{T}~\text{is a triangulation of }M\}, \] where denotes the dual graph of…
ImpFlows generalize normalizing flows by implicitly defining transformations.