Related papers: OCDE: Odds Conditional Density Estimator

End-to-end learning of dynamical systems with black-box models, such as neural ordinary differential equations (ODEs), provides a flexible framework for learning dynamics from data without prescribing a mathematical model for the dynamics.…

Ordinary differential equations (ODE's) are widespread models in physics, chemistry and biology. In particular, this mathematical formalism is used for describing the evolution of complex systems and it might consist of high-dimensional…

We introduce SCDE, a dataset to evaluate the performance of computational models through sentence prediction. SCDE is a human-created sentence cloze dataset, collected from public school English examinations. Our task requires a model to…

Nonlinear ordinary differential equations (ODEs) are powerful tools for modeling real-world dynamical systems. However, propagating initial state uncertainty through nonlinear dynamics, especially when the ODE is unknown and learned from…

Due to the inability to interact with the environment, offline reinforcement learning (RL) methods face the challenge of estimating the Out-of-Distribution (OOD) points. Existing methods for addressing this issue either control policy to…

Probabilistic solvers for ordinary differential equations (ODEs) have emerged as an efficient framework for uncertainty quantification and inference on dynamical systems. In this work, we explain the mathematical assumptions and detailed…

Ordinal cumulative probability models (CPMs) -- also known as cumulative link models -- such as the proportional odds regression model are typically used for discrete ordered outcomes, but can accommodate both continuous and mixed…

Random forests is a common non-parametric regression technique which performs well for mixed-type unordered data and irrelevant features, while being robust to monotonic variable transformations. Standard random forests, however, do not…

Multivariate density estimation is a popular technique in statistics with wide applications including regression models allowing for heteroskedasticity in conditional variances. The estimation problems become more challenging when…

Designing and analyzing optimization methods via continuous-time models expressed as ordinary differential equations (ODEs) is a promising approach for its intuitiveness and simplicity. A key concern, however, is that the convergence rates…

Given $iid$ observations from an unknown absolute continuous distribution defined on some domain $\Omega$, we propose a nonparametric method to learn a piecewise constant function to approximate the underlying probability density function.…

Conditional Variance Estimation (CVE) is a novel sufficient dimension reduction (SDR) method for additive error regressions with continuous predictors and link function. It operates under the assumption that the predictors can be replaced…

This paper addresses imitation learning for motion prediction problem in autonomous driving, especially in multi-agent setting. Different from previous methods based on GAN, we present the conditional latent ordinary differential equation…

Inferring the parameters of ordinary differential equations (ODEs) from noisy observations is an important problem in many scientific fields. Currently, most parameter estimation methods that bypass numerical integration tend to rely on…

Let $\textbf{X} = (X_1,\ldots, X_p)$ be a stochastic vector having joint density function $f_{\textbf{X}}(x)$ with partitions $\textbf{X}_1 = (X_1,\ldots, X_k)$ and $\textbf{X}_2 = (X_{k+1},\ldots, X_p)$. A new method for estimating the…

Since the advent of the ``Neural Ordinary Differential Equation (Neural ODE)'' paper, learning ODEs with deep learning has been applied to system identification, time-series forecasting, and related areas. Exploiting the diffeomorphic…

There are several estimators of conditional probability from observed frequencies of features. In this paper, we propose using the lower limit of confidence interval on posterior distribution determined by the observed frequencies to…

Stiff systems of ordinary differential equations (ODEs) are pervasive in many science and engineering fields, yet standard neural ODE approaches struggle to learn them. This limitation is the main barrier to the widespread adoption of…

In recent years, kernel density estimation has been exploited by computer scientists to model machine learning problems. The kernel density estimation based approaches are of interest due to the low time complexity of either O(n) or…

Accurate reporting and forecasting of PM2.5 concentration are important for improving public health. In this paper, we propose a daily prediction method of PM2.5 concentration by using data-driven ordinary differential equation (ODE)…