In this paper, we focus on the modification of policies that can lead to movement patterns and directional guidance of occupants, which are represented as agents in a 3D simulation engine. We demonstrate an optimization method that improves a spatial distancing metric by modifying the navigation graph by introducing a measure of spatial distancing of agents as a function of agent density (i.e., occupancy). Our optimization framework utilizes such metrics as the target function, using a hybrid approach of combining genetic algorithm and simulated annealing. We show that within our framework, the simulation-optimization process can help to improve spatial distancing between agents by optimizing the navigation policies for a given indoor environment.

Cluster analysis is a popular method for identifying subgroups within a population, but the results are often challenging to interpret and action. Supervised clustering leverages SHAP values to identify better-separated clusters using a more structured representation of the data. This article demonstrates the benefits of supervised clustering with an example based on simulated data. I provide a simple illustration of a methodology I applied to COVID-19 symptom clustering for a paper at the ECML PKDD 2021 conference. This article assumes a basic understanding of SHAP, which is a technique for deconstructing a machine learning model's predictions into a sum of contributions from each of its input variables.

Databricks is a business software startup that provides Data Engineering tools for processing and transforming massive amounts of data to develop machine learning models. Traditional Big Data procedures are not only slow to complete jobs but also take more time to build up Hadoop clusters. However, Databricks is built on top of distributed Cloud computing infrastructures like Azure, AWS, or Google Cloud, which allow programmes to execute on CPUs or GPUs according to analytical needs. In this article, we will be learning about building a machine learning model in Databricks. Following are the topics to be covered. In this article, we will be building a multivariate linear regression model for predicting the charges on insurance offered by the company based on different features.

XGBoost, short for "Extreme Gradient Boosting," is one of the strongest machine learning algorithms for handling tabular data, a well-deserved reputation due to its success in winning numerous Kaggle competitions. XGBoost is an ensemble machine learning algorithm that usually consists of Decision Trees. The Decision Trees that make up XGBoost are individually referred to as gbtree, short for "gradient boosted tree." The first Decision Tree in the XGBoost ensemble is the base learner whose mistakes all subsequent trees learn from. Although Decision Trees are generally preferred as base learners due to their excellent ensemble scores, in some cases, alternative base learners may outperform them.

Atmospheric Extreme Events (EEs) cause severe damages to human societies and ecosystems. The frequency and intensity of EEs and other associated events are increasing in the current climate change and global warming risk. The accurate prediction, characterization, and attribution of atmospheric EEs is therefore a key research field, in which many groups are currently working by applying different methodologies and computational tools. Machine Learning (ML) methods have arisen in the last years as powerful techniques to tackle many of the problems related to atmospheric EEs. This paper reviews the ML algorithms applied to the analysis, characterization, prediction, and attribution of the most important atmospheric EEs. A summary of the most used ML techniques in this area, and a comprehensive critical review of literature related to ML in EEs, are provided. A number of examples is discussed and perspectives and outlooks on the field are drawn.

With graduation season just around the corner, I've had a few family members ask how often they would use the information they learned over the years. One cousin, in particular, was not a huge fan of math. However, he built his gaming PC and otherwise enjoys learning about computer hardware. At one point it was mentioned that computers will do all the necessary math, so why memorize formulas? While I saw his perspective to a degree, math is a building block to learning more about computers especially, and being able to verify results never hurt as a programmer. That train thought brought me back to Algebra 1, where I remember learning about graphs and modeling methods such as Linear Regression.

Let us start with an easy example, say you are teaching a kid to differentiate dogs from cats. How would you do it? You may show him/her a dog and say "here is a dog" and when you encounter a cat you would point it out as a cat. When you show the kid enough dogs and cats, he may learn to differentiate between them. If he is trained well, he may be able to recognise different breeds of dogs which he hasn't even seen. Similarly, in Supervised Learning, we have two sets of variables.

Dimensionality reduction algorithms reduce dimension while retaining information present in the high-dimensional data. What makes each method unique is the type of information it preserves in the lower dimension. We want our colors arranged such that similar colors are mapped close to each other. We map the RGB data to a one-dimensional array and sort it. Different methods use different objective functions to reduce dimensions.

Generalization is one of the most important problems in deep learning (DL). In the overparameterized regime in neural networks, there exist many low-loss solutions that fit the training data equally well. The key question is which solution is more generalizable. Empirical studies showed a strong correlation between flatness of the loss landscape at a solution and its generalizability, and stochastic gradient descent (SGD) is crucial in finding the flat solutions. To understand how SGD drives the learning system to flat solutions, we construct a simple model whose loss landscape has a continuous set of degenerate (or near degenerate) minima. By solving the Fokker-Planck equation of the underlying stochastic learning dynamics, we show that due to its strong anisotropy the SGD noise introduces an additional effective loss term that decreases with flatness and has an overall strength that increases with the learning rate and batch-to-batch variation. We find that the additional landscape-dependent SGD-loss breaks the degeneracy and serves as an effective regularization for finding flat solutions. Furthermore, a stronger SGD noise shortens the convergence time to the flat solutions. However, we identify an upper bound for the SGD noise beyond which the system fails to converge. Our results not only elucidate the role of SGD for generalization they may also have important implications for hyperparameter selection for learning efficiently without divergence.

We analyze the dynamics of large batch stochastic gradient descent with momentum (SGD+M) on the least squares problem when both the number of samples and dimensions are large. In this setting, we show that the dynamics of SGD+M converge to a deterministic discrete Volterra equation as dimension increases, which we analyze. We identify a stability measurement, the implicit conditioning ratio (ICR), which regulates the ability of SGD+M to accelerate the algorithm. When the batch size exceeds this ICR, SGD+M converges linearly at a rate of $\mathcal{O}(1/\sqrt{\kappa})$, matching optimal full-batch momentum (in particular performing as well as a full-batch but with a fraction of the size). For batch sizes smaller than the ICR, in contrast, SGD+M has rates that scale like a multiple of the single batch SGD rate. We give explicit choices for the learning rate and momentum parameter in terms of the Hessian spectra that achieve this performance.