Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userBetter Conditional Density Estimation for Neural Networks
148
0
0.0
(
0
)
Added by
Wesley Tansey
Publication date
2016
fields
Mathematical Statistics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
The vast majority of the neural network literature focuses on predicting point values for a given set of response variables, conditioned on a feature vector. In many cases we need to model the full joint conditional distribution over the response variables rather than simply making point predictions. In this paper, we present two novel approaches to such conditional density estimation (CDE): Multiscale Nets (MSNs) and CDE Trend Filtering. Multiscale nets transform the CDE regression task into a hierarchical classification task by decomposing the density into a series of half-spaces and learning boolean probabilities of each split. CDE Trend Filtering applies a k-th order graph trend filtering penalty to the unnormalized logits of a multinomial classifier network, with each edge in the graph corresponding to a neighboring point on a discretized version of the density. We compare both methods against plain multinomial classifier networks and mixture density networks (MDNs) on a simulated dataset and three real-world datasets. The results suggest the two methods are complementary: MSNs work well in a high-data-per-feature regime and CDE-TF is well suited for few-samples-per-feature scenarios where overfitting is a primary concern.
rate research
Read More
Given a set of empirical observations, conditional density estimation aims to capture the statistical relationship between a conditional variable $mathbf{x}$ and a dependent variable $mathbf{y}$ by modeling their conditional probability $p(mathbf{y}|mathbf{x})$. The paper develops best practices for conditional density estimation for finance applications with neural networks, grounded on mathematical insights and empirical evaluations. In particular, we introduce a noise regularization and data normalization scheme, alleviating problems with over-fitting, initialization and hyper-parameter sensitivity of such estimators. We compare our proposed methodology with popular semi- and non-parametric density estimators, underpin its effectiveness in various benchmarks on simulated and Euro Stoxx 50 data and show its superior performance. Our methodology allows to obtain high-quality estimators for statistical expectations of higher moments, quantiles and non-linear return transformations, with very little assumptions about the return dynamic.
Modelling statistical relationships beyond the conditional mean is crucial in many settings. Conditional density estimation (CDE) aims to learn the full conditional probability density from data. Though highly expressive, neural network based CDE models can suffer from severe over-fitting when trained with the maximum likelihood objective. Due to the inherent structure of such models, classical regularization approaches in the parameter space are rendered ineffective. To address this issue, we develop a model-agnostic noise regularization method for CDE that adds random perturbations to the data during training. We demonstrate that the proposed approach corresponds to a smoothness regularization and prove its asymptotic consistency. In our experiments, noise regularization significantly and consistently outperforms other regularization methods across seven data sets and three CDE models. The effectiveness of noise regularization makes neural network based CDE the preferable method over previous non- and semi-parametric approaches, even when training data is scarce.
Random forests is a common non-parametric regression technique which performs well for mixed-type data and irrelevant covariates, while being robust to monotonic variable transformations. Existing random forest implementations target regression or classification. We introduce the RFCDE package for fitting random forest models optimized for nonparametric conditional density estimation, including joint densities for multiple responses. This enables analysis of conditional probability distributions which is useful for propagating uncertainty and of joint distributions that describe relationships between multiple responses and covariates. RFCDE is released under the MIT open-source license and can be accessed at https://github.com/tpospisi/rfcde . Both R and Pyth
Modeling complex conditional distributions is critical in a variety of settings. Despite a long tradition of research into conditional density estimation, current methods employ either simple parametric forms or are difficult to learn in practice. This paper employs normalising flows as a flexible likelihood model and presents an efficient method for fitting them to complex densities. These estimators must trade-off between modeling distributional complexity, functional complexity and heteroscedasticity without overfitting. We recognize these trade-offs as modeling decisions and develop a Bayesian framework for placing priors over these conditional density estimators using variational Bayesian neural networks. We evaluate this method on several small benchmark regression datasets, on some of which it obtains state of the art performance. Finally, we apply the method to two spatial density modeling tasks with over 1 million datapoints using the New York City yellow taxi dataset and the Chicago crime dataset.
We present a method for conditional time series forecasting based on an adaptation of the recent deep convolutional WaveNet architecture. The proposed network contains stacks of dilated convolutions that allow it to access a broad range of history when forecasting, a ReLU activation function and conditioning is performed by applying multiple convolutional filters in parallel to separate time series which allows for the fast processing of data and the exploitation of the correlation structure between the multivariate time series. We test and analyze the performance of the convolutional network both unconditionally as well as conditionally for financial time series forecasting using the S&P500, the volatility index, the CBOE interest rate and several exchange rates and extensively compare it to the performance of the well-known autoregressive model and a long-short term memory network. We show that a convolutional network is well-suited for regression-type problems and is able to effectively learn dependencies in and between the series without the need for long historical time series, is a time-efficient and easy to implement alternative to recurrent-type networks and tends to outperform linear and recurrent models.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
