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 develops a slice sampler for Bayesian linear regression models with arbitrary priors. The new sampler has two advantages over current approaches. One, it is faster than many custom implementations that rely on auxiliary latent variables, if the number of regressors is large. Two, it can be used with any prio…
In recent years, several methods have been proposed for the discovery of causal structure from non-experimental data (Spirtes et al. 2000; Pearl 2000). Such methods make various assumptions on the data generating process to facilitate its identification from purely observational data. Continuing this line of research, …
In this work, we consider the identifiability assumption of Gaussian linear structural equation models (SEMs) in which each variable is determined by a linear function of its parents plus normally distributed error. It has been shown that linear Gaussian structural equation models are fully identifiable if all error va…
Restricted Boltzmann Machine (RBM) is a bipartite graphical model that is used as the building block in energy-based deep generative models. Due to numerical stability and quantifiability of the likelihood, RBM is commonly used with Bernoulli units. Here, we consider an alternative member of exponential family RBM with…
The paper develops ML algorithms for calibrating credit rating transition models for high and low default portfolios.
problem Calibration of credit rating transition models for high and low default portfolios.
method Developed Maximum likelihood (ML) algorithms, including Laplace approximation for high-default portfolios and particle filter with Gaussian process regression for low-default portfolios.
result Both algorithms produce accurate approximations of the likelihood function and ML estimates of model parameters.
Statistical arbitrage strategies, such as pairs trading and its generalizations, rely on the construction of mean-reverting spreads enjoying a certain degree of predictability. Gaussian linear state-space processes have recently been proposed as a model for such spreads under the assumption that the observed process is…
Sparse representations have proven their efficiency in solving a wide class of inverse problems encountered in signal and image processing. Conversely, enforcing the information to be spread uniformly over representation coefficients exhibits relevant properties in various applications such as digital communications. A…
Conformal prediction uses past experience to determine precise levels of confidence in new predictions. Given an error probability ε, together with a method that makes a prediction y^ of a label y, it produces a set of labels, typically containing y^, that also contains y with probability 1−ε. Con…
We develop a projected Nesterov's proximal-gradient (PNPG) approach for sparse signal reconstruction that combines adaptive step size with Nesterov's momentum acceleration. The objective function that we wish to minimize is the sum of a convex differentiable data-fidelity (negative log-likelihood (NLL)) term and a conv…
Statistical inference can be computationally prohibitive in ultrahigh-dimensional linear models. Correlation-based variable screening, in which one leverages marginal correlations for removal of irrelevant variables from the model prior to statistical inference, can be used to overcome this challenge. Prior works on co…
We introduce a procedure for conditional density estimation under logarithmic loss, which we call SMP (Sample Minmax Predictor). This estimator minimizes a new general excess risk bound for statistical learning. On standard examples, this bound scales as d/n with d the model dimension and n the sample size, and c…
We study a family of sparse estimators defined as minimizers of some empirical Lipschitz loss function -- which include the hinge loss, the logistic loss and the quantile regression loss -- with a convex, sparse or group-sparse regularization. In particular, we consider the L1 norm on the coefficients, its sorted Slope…
Random linear mappings are widely used in modern signal processing, compressed sensing and machine learning. These mappings may be used to embed the data into a significantly lower dimension while at the same time preserving useful information. This is done by approximately preserving the distances between data points,…
Develops efficient algorithms for learning latent-variable models using implicit moment tensor computation.
problem Learning latent-variable models with moment tensors of super-constant degree.
method Implicit moment tensor computation for general models, extending previous work on clustering mixtures of spherical Gaussians.
result First poly(d, k) time learning algorithms for various models including mixtures of linear regressions, spherical Gaussians, and positive linear combinations of non-linear activations.
This paper considers control systems defined on Lie algebroids. After deriving basic controllability tests for general control systems, we specialize our discussion to the class of mechanical control systems on Lie algebroids. This class of systems includes mechanical systems subject to holonomic and nonholonomic const…
Systemic risk refers to the risk that the financial system is susceptible to failures due to the characteristics of the system itself. The tremendous cost of systemic risk requires the design and implementation of tools for the efficient macroprudential regulation of financial institutions. The current paper proposes a…