The Newsvendor problem is a fundamental model in inventory management (Rossi, 2021) that accommodates both known (Dvoretzky et al., 1952a) and unknown (Dvoretzky et al., 1952b) demand distributions. Since its inception (Edgewort, 1888), it has been widely applied in inventory control and policy-making (Arrow et al., 1951), as well as various real-world situations (Choi, 2012; Chen et al., 2016). Its simplicity stems from considering a single product for sale, for which the optimal initial stock level must be determined to satisfy forecasted demand over a given period without restocking. The interplay among purchasing cost, selling price, and stock ordered at the beginning of the period determines the inventory management policies (Whitin, 1952; Rosenblatt, 1954; Petruzzi and Dada, 1999). The model has been extensively studied for single stock-keeping units (SKUs). Electronic marketplaces introduce an extra complication to the problem, as they need to manage a large number of SKUs at distribution centers alongside highly variable demand received through electronic platforms.

The recent M5 competition has advanced the state-of-the-art in retail forecasting. However, we notice important differences between the competition challenge and the challenges we face in a large e-commerce company. The datasets in our scenario are larger (hundreds of thousands of time series), and e-commerce can afford to have a larger assortment than brick-and-mortar retailers, leading to more intermittent data. To scale to larger dataset sizes with feasible computational effort, firstly, we investigate a two-layer hierarchy and propose a top-down approach to forecasting at an aggregated level with less amount of series and intermittency, and then disaggregating to obtain the decision-level forecasts. Probabilistic forecasts are generated under distributional assumptions. Secondly, direct training at the lower level with subsamples can also be an alternative way of scaling. Performance of modelling with subsets is evaluated with the main dataset. Apart from a proprietary dataset, the proposed scalable methods are evaluated using the Favorita dataset and the M5 dataset. We are able to show the differences in characteristics of the e-commerce and brick-and-mortar retail datasets. Notably, our top-down forecasting framework enters the top 50 of the original M5 competition, even with models trained at a higher level under a much simpler setting.

Measuring sales performance is a crucial aspect of running a successful business. Accurately tracking and analyzing sales data helps companies understand their strengths and weaknesses, perform forecasts, identify trends, and make informed decisions that drive growth. In this article, I will illuminate how some simple statistical models can be used for measuring sales performance. Whether it is a small or enterprise sales team, simple quantitative techniques can be used to provide valuable sales insights or draw attention to areas of need. After reading this article, you will see various examples how simple models are applied in real life scenarios. Note: All the images in the article were generated by Artificial Intelligence using Stable Diffusion 2.x.

Single cell RNA sequencing (scRNA-Seq) is being widely used in biomedical research and generated enormous volume and diversity of data. The raw data contain multiple types of noise and technical artifacts, which need thorough cleaning. Existing denoising and imputation methods largely focus on a single type of noise (i.e., dropouts) and have strong distribution assumptions which greatly limit their performance and application. Here we design and develop the AutoClass model, integrating two deep neural network components, an autoencoder, and a classifier, as to maximize both noise removal and signal retention. AutoClass is distribution agnostic as it makes no assumption on specific data distributions, hence can effectively clean a wide range of noise and artifacts. AutoClass outperforms the state-of-art methods in multiple types of scRNA-Seq data analyses, including data recovery, differential expression analysis, clustering analysis, and batch effect removal. Importantly, AutoClass is robust on key hyperparameter settings including bottleneck layer size, pre-clustering number and classifier weight. We have made AutoClass open source at: https://github.com/datapplab/AutoClass . Single cell RNA sequencing (scRNA-Seq) is widely used in biomedical research. Here the authors develop a novel AI model-AutoClass, which effectively cleans a wide range of noise and artifacts in scRNA-Seq data and improves downstream analyses.

This method has achieved excellent predictive performance in many fields and has exhibited many advantages, and is consequently considered especially suitable for the statistical analysis of big data. However, this method is limited because its loss function must be convex. For many scenario-specific problems, such as non-life insurance pricing, the distribution of predictor variables is often heavytailed, so the optimal prediction performance may not be obtained by setting convex loss functions. Simultaneously, it is important to estimate the probability distribution of predictor variables. When the set parametric probability distribution contains more than two parameters, it may be necessary to model multiple parameters to obtain better prediction performance. Therefore, a more generalized regularized tree boosting method is required to make the loss function not limited to the convex function while modelling the tree boosting for multiple parameters, to adapt to the most common parametric probability distributions.

The M5 competition uncertainty track aims for probabilistic forecasting of sales of thousands of Walmart retail goods. We show that the M5 competition data faces strong overdispersion and sporadic demand, especially zero demand. We discuss resulting modeling issues concerning adequate probabilistic forecasting of such count data processes. Unfortunately, the majority of popular prediction methods used in the M5 competition (e.g. lightgbm and xgboost GBMs) fails to address the data characteristics due to the considered objective functions. The distributional forecasting provides a suitable modeling approach for to the overcome those problems. The GAMLSS framework allows flexible probabilistic forecasting using low dimensional distributions. We illustrate, how the GAMLSS approach can be applied for the M5 competition data by modeling the location and scale parameter of various distributions, e.g. the negative binomial distribution. Finally, we discuss software packages for distributional modeling and their drawback, like the R package gamlss with its package extensions, and (deep) distributional forecasting libraries such as TensorFlow Probability.

Successful and accurate modelling of level difficulty is a fundamental component of the operationalisation of player experience as difficulty is one of the most important and commonly used signals for content design and adaptation. In games that feature intermediate milestones, such as completable areas or levels, difficulty is often defined by the probability of completion or completion rate; however, this operationalisation is limited in that it does not describe the behaviour of the player within the area. In this research work, we formalise a model of level difficulty for puzzle games that goes beyond the classical probability of success. We accomplish this by describing the distribution of actions performed within a game level using a parametric statistical model thus creating a richer descriptor of difficulty. The model is fitted and evaluated on a dataset collected from the game Lily's Garden by Tactile Games, and the results of the evaluation show that the it is able to describe and explain difficulty in a vast majority of the levels.

Reinforcement learning algorithms are frequently categorized by whether they predict future states at any point in their decision-making process. Those that do are called model-based, and those that do not are dubbed model-free. This classification is so common that we mostly take it for granted these days; I am guilty of using it myself. However, this distinction is not as clear-cut as it may initially seem. In this post, I will talk about an alternative view that emphases the mechanism of prediction instead of the content of prediction.

As the large amount of sequencing data accumulated in past decades and it is still accumulating, we need to handle the more and more sequencing data. As the fast development of the computing technologies, we now can handle a large amount of data by a reasonable of time using the neural network based model. This tutorial will introduce the the mathematical model of the single cell variational inference (scVI), which use the variational auto-encoder (building on the neural networks) to learn the distribution of the data to gain insights. It was written for beginners in the simple and intuitive way with many deduction details to encourage more researchers into this field. As the computer technology evolves rapidly, we can tackle more and more complex problem by finding a suitable function taking millions of parameters to model the key part of the problems.

From the distributional characterizations that lie at the heart of Stein's method we derive explicit formulae for the mass functions of discrete probability laws that identify those distributions. These identities are applied to develop tools for the solution of statistical problems. Our characterizations, and hence the applications built on them, do not require any knowledge about normalization constants of the probability laws. We discuss several examples where this lack of feasibility of the normalization constant is a built-in feature. To demonstrate that our statistical methods are sound, we provide comparative simulation studies for the testing of fit to the Poisson distribution and for parameter estimation of the negative binomial family when both parameters are unknown. We also consider the problem of parameter estimation for discrete exponential-polynomial models which generally are non-normalized.