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.
We extend the Fourier cosine method to discrete probability distributions, achieving faster convergence rates.
New formulae identify discrete probability laws without needing normalization constants.
Sharp bounds for high-probability estimation of discrete distributions.
Improved bounds for discrete probability distribution estimation under the ℓ∞ norm.
Refined analysis of Mitra's algorithm for discrete mixtures.
SDE automatically recovers interpretable discrete distributions.
In this expository paper we illustrate the generality of game theoretic probability protocols of Shafer and Vovk (2001) in finite-horizon discrete games. By restricting ourselves to finite-horizon discrete games, we can explicitly describe how discrete distributions with finite support and the discrete pricing formulas…
Study error bounds in evaluating distributional computational graphs.
In this paper a quantitative analysis of the ruin probability in finite time of discrete risk process with proportional reinsurance and investment of finance surplus is focused on. It is assumed that the total loss on a unit interval has a light-tailed distribution -- exponential distribution and a heavy-tailed distrib…
Investigates statistical properties of perturb-softmax and perturb-argmax distributions.
Probability distributions produced by the cross-entropy loss for ordinal classification problems can possess undesired properties. We propose a straightforward technique to constrain discrete ordinal probability distributions to be unimodal via the use of the Poisson and binomial probability distributions. We evaluate …
The paper develops approximations for Pearson's chi-square statistic and applies them to confidence intervals.
Representations based on random walks can exploit discrete data distributions for clustering and classification. We extend such representations from discrete to continuous distributions. Transition probabilities are now calculated using a diffusion equation with a diffusion coefficient that inversely depends on the dat…
A method for diffusion on probability simplex for generative models.
Optimal testing of discrete distributions with high probability, achieving sample complexity bounds.
Exact Bayesian inference for discrete models using probability generating functions.
Sequence-to-sequence text-to-speech (TTS) is dominated by soft-attention-based methods. Recently, hard-attention-based methods have been proposed to prevent fatal alignment errors, but their sampling method of discrete alignment is poorly investigated. This research investigates various combinations of sampling methods…
Proves hardness of semi-discrete optimal transport and proposes regularization methods.
A new method for categorical variational inference using discrete normalizing flows.
This paper studies geometrical structure of the manifold of escort probability distributions and shows its new applicability to information science. In order to realize escort probabilities we use a conformal transformation that flattens so-called alpha-geometry of the space of discrete probability distributions, which…
Flow based models such as Real NVP are an extremely powerful approach to density estimation. However, existing flow based models are restricted to transforming continuous densities over a continuous input space into similarly continuous distributions over continuous latent variables. This makes them poorly suited for m…
New algorithms for efficient return distribution approximation in reinforcement learning.
We describe discrete restricted Boltzmann machines: probabilistic graphical models with bipartite interactions between visible and hidden discrete variables. Examples are binary restricted Boltzmann machines and discrete naive Bayes models. We detail the inference functions and distributed representations arising in th…
Moate Simulation improves accuracy and speed of financial derivative pricing.
Unified discrete diffusion for categorical data simplifies training and sampling.
Generative model for joint discrete distributions using randomized assignment flows.
In quantitative finance, it is often necessary to analyze the distribution of the sum of specific functions of observed values at discrete points of an underlying process. Examples include the probability density function, the hedging error, the Asian option, and statistical hypothesis testing. We propose a method to c…
Paper proposes DAG-DB for learning discrete DAGs via backpropagation.
The discrete sum of geometric Brownian motions plays an important role in modeling stochastic annuities in insurance. It also plays a pivotal role in the pricing of Asian options in mathematical finance. In this paper, we study the probability distributions of the infinite sum of geometric Brownian motions, the sum of …
This work bounds the generalization error of private algorithms for discrete data.
This paper proposes an active learning-based Gaussian process (AL-GP) metamodelling method to estimate the cumulative as well as complementary cumulative distribution function (CDF/CCDF) for forward uncertainty quantification (UQ) problems. Within the field of UQ, previous studies focused on developing AL-GP approaches…
We propose a correlated stochastic process of which the novel non-Gaussian probability mass function is constructed by exactly solving moment generating function. The calculation of cumulants and auto-correlation shows that the process is convergent and scale invariant in the large but finite number limit. We demonstra…
Novel approach for estimating joint probability densities using tensor decompositions and dictionaries.
We propose a method to classify the causal relationship between two discrete variables given only the joint distribution of the variables, acknowledging that the method is subject to an inherent baseline error. We assume that the causal system is acyclicity, but we do allow for hidden common causes. Our algorithm presu…
New bounds for generative models under weaker assumptions.
The reparameterization trick enables optimizing large scale stochastic computation graphs via gradient descent. The essence of the trick is to refactor each stochastic node into a differentiable function of its parameters and a random variable with fixed distribution. After refactoring, the gradients of the loss propag…
Optimizes risk-neutral probabilities for derivative pricing.
Paper studies matching of samples from two distributions with a Gibbs probability weight.
We present a deep learning model, DE-LSTM, for the simulation of a stochastic process with an underlying nonlinear dynamics. The deep learning model aims to approximate the probability density function of a stochastic process via numerical discretization and the underlying nonlinear dynamics is modeled by the Long Shor…
Wasserstein gradient flows are continuous time dynamics that define curves of steepest descent to minimize an objective function over the space of probability measures (i.e., the Wasserstein space). This objective is typically a divergence w.r.t. a fixed target distribution. In recent years, these continuous time dynam…
This paper shows that one cannot learn the probability of rare events without imposing further structural assumptions. The event of interest is that of obtaining an outcome outside the coverage of an i.i.d. sample from a discrete distribution. The probability of this event is referred to as the "missing mass". The impo…
We present an approach to deep estimation of discrete conditional probability distributions. Such models have several applications, including generative modeling of audio, image, and video data. Our approach combines two main techniques: dyadic partitioning and graph-based smoothing of the discrete space. By recursivel…
Estimates mode of discrete distributions with fewer samples.
In this paper, we propose the discrete time Compound Beta-Binomial Risk Model with by-claims, delayed by-claims and randomized dividends. We then analyze the Gerber-Shiu function for the cases where the dividend threshold and under the assumption that the constant discount rate . More specifical…
Deep neural networks can approximate any target probability distribution given certain conditions.
We consider the problem of the estimation of a high-dimensional probability distribution from i.i.d. samples of the distribution using model classes of functions in tree-based tensor formats, a particular case of tensor networks associated with a dimension partition tree. The distribution is assumed to admit a density …
This paper finds a unique partition of a sample space for estimating continuous distributions.
Continuous time models in the theory of real options give explicit formulas for optimal exercise strategies when options are simple and the price of an underlying asset follows a geometric Brownian motion. This paper suggests a general, computationally simple approach to real options in discrete time. Explicit formulas…