arXiv subjects

Konstantin Posch

Publications and source records attributed to Konstantin Posch.

5 recordsLinked to original sources

arXiv2021

A Bayesian Approach for Predicting Food and Beverage Sales in Staff Canteens and Restaurants

Accurate demand forecasting is one of the key aspects for successfully managing restaurants and staff canteens. In particular, properly predicting future sales of menu items allows a precise ordering of food stock. From an environmental point of view, this ensures maintaining a low level of pre-consumer food waste, while from the managerial point of view, this is critical to guarantee the profitability of the restaurant. Hence, we are interested in predicting future values of the daily sold quantities of given menu items. The corresponding time series show multiple strong seasonalities, trend changes, data gaps, and outliers. We propose a forecasting approach that is solely based on the data retrieved from Point of Sales systems and allows for a straightforward human interpretation. Therefore, we propose two generalized additive models for predicting the future sales. In an extensive evaluation, we consider two data sets collected at a casual restaurant and a large staff canteen consisting of multiple time series, that cover a period of 20 months, respectively. We show that the proposed models fit the features of the considered restaurant data. Moreover, we compare the predictive performance of our method against the performance of other well-established forecasting approaches.

stat.AP↗

arXiv2021

Variable Selection Using Nearest Neighbor Gaussian Processes

We introduce a novel Bayesian approach for variable selection using Gaussian process regression, which is crucial for enhancing interpretability and model regularization. Our method employs nearest neighbor Gaussian processes, serving as scalable approximations of classical Gaussian processes. Variable selection is achieved by conditioning the process mean and covariance function on a random set that represents the indices of contributing variables. A priori beliefs regarding this set control the variable selection, while reference priors are assigned to the remaining model parameters, ensuring numerical robustness in the process covariance matrix. We propose a Metropolis-Within-Gibbs algorithm for model inference. Evaluation using simulated data, a computer experiment approximation, and two real-world data sets demonstrate the effectiveness of our approach.

stat.CO↗

arXiv2019

Correlated Parameters to Accurately Measure Uncertainty in Deep Neural Networks

In this article a novel approach for training deep neural networks using Bayesian techniques is presented. The Bayesian methodology allows for an easy evaluation of model uncertainty and additionally is robust to overfitting. These are commonly the two main problems classical, i.e. non-Bayesian, architectures have to struggle with. The proposed approach applies variational inference in order to approximate the intractable posterior distribution. In particular, the variational distribution is defined as product of multiple multivariate normal distributions with tridiagonal covariance matrices. Each single normal distribution belongs either to the weights, or to the biases corresponding to one network layer. The layer-wise a posteriori variances are defined based on the corresponding expectation values and further the correlations are assumed to be identical. Therefore, only a few additional parameters need to be optimized compared to non-Bayesian settings. The novel approach is successfully evaluated on basis of the popular benchmark datasets MNIST and CIFAR-10.

cs.LG↗

arXiv2019

A novel Bayesian approach for variable selection in linear regression models

We propose a novel Bayesian approach to the problem of variable selection in multiple linear regression models. In particular, we present a hierarchical setting which allows for direct specification of a-priori beliefs about the number of nonzero regression coefficients as well as a specification of beliefs that given coefficients are nonzero. To guarantee numerical stability, we adopt a $g$-prior with an additional ridge parameter for the unknown regression coefficients. In order to simulate from the joint posterior distribution an intelligent random walk Metropolis-Hastings algorithm which is able to switch between different models is proposed. Testing our algorithm on real and simulated data illustrates that it performs at least on par and often even better than other well-established methods. Finally, we prove that under some nominal assumptions, the presented approach is consistent in terms of model selection.

stat.CO↗

arXiv2019

Variational Inference to Measure Model Uncertainty in Deep Neural Networks

We present a novel approach for training deep neural networks in a Bayesian way. Classical, i.e. non-Bayesian, deep learning has two major drawbacks both originating from the fact that network parameters are considered to be deterministic. First, model uncertainty cannot be measured thus limiting the use of deep learning in many fields of application and second, training of deep neural networks is often hampered by overfitting. The proposed approach uses variational inference to approximate the intractable a posteriori distribution on basis of a normal prior. The variational density is designed in such a way that the a posteriori uncertainty of the network parameters is represented per network layer and depending on the estimated parameter expectation values. This way, only a few additional parameters need to be optimized compared to a non-Bayesian network. We apply this Bayesian approach to train and test the LeNet architecture on the MNIST dataset. Compared to classical deep learning, the test error is reduced by 15%. In addition, the trained model contains information about the parameter uncertainty in each layer. We show that this information can be used to calculate credible intervals for the prediction and to optimize the network architecture for a given training data set.

stat.ML↗