A common assumption in generative models is that the generator immerses the latent space into a Euclidean ambient space. Instead, we consider the ambient space to be a Riemannian manifold, which allows for encoding domain knowledge through the associated Riemannian metric. Shortest paths can then be defined accordingly in the latent space to both follow the learned manifold and respect the ambient geometry. Through careful design of the ambient metric we can ensure that shortest paths are well-behaved even for deterministic generators that otherwise would exhibit a misleading bias. Experimentally we show that our approach improves interpretability of learned representations both using stochastic and deterministic generators.

The ability to infer map variables and estimate pose is crucial to the operation of autonomous mobile robots. In most cases the shared dependency between these variables is modeled through a multivariate Gaussian distribution, but there are many situations where that assumption is unrealistic. Our paper shows how it is possible to relax this assumption and perform simultaneous localization and mapping (SLAM) with a larger class of distributions, whose multivariate dependency is represented with a copula model. We integrate the distribution model with copulas into a Sequential Monte Carlo estimator and show how unknown model parameters can be learned through gradient-based optimization. We demonstrate our approach is effective in settings where Gaussian assumptions are clearly violated, such as environments with uncertain data association and nonlinear transition models.

Dynamic discrete choice models are used to estimate the intertemporal preferences of an agent as described by a reward function based upon observable histories of states and implemented actions. However, in many applications, such as reliability and healthcare, the system state is partially observable or hidden (e.g., the level of deterioration of an engine, the condition of a disease), and the decision maker only has access to information imperfectly correlated with the true value of the hidden state. In this paper, we consider the estimation of a dynamic discrete choice model with state variables and system dynamics that are hidden (or partially observed) to both the agent and the modeler, thus generalizing Rust's model to partially observable cases. We analyze the structural properties of the model and prove that this model is still identifiable if the cardinality of the state space, the discount factor, the distribution of random shocks, and the rewards for a given (reference) action are given. We analyze both theoretically and numerically the potential mis-specification errors that may be incurred when Rust's model is improperly used in partially observable settings. We further apply the developed model to a subset of Rust's dataset for bus engine mileage and replacement decisions. The results show that our model can improve model fit as measured by the $\log$-likelihood function by $17.7\%$ and the $\log$-likelihood ratio test shows that our model statistically outperforms Rust's model. Interestingly, our hidden state model also reveals an economically meaningful route assignment behavior in the dataset which was hitherto ignored, i.e. routes with lower mileage are assigned to buses believed to be in worse condition.

We introduce a novel rule-based approach for handling regression problems. The new methodology carries elements from two frameworks: (i) it provides information about the uncertainty of the parameters of interest using Bayesian inference, and (ii) it allows the incorporation of expert knowledge through rule-based systems. The blending of those two different frameworks can be particularly beneficial for various domains (e.g. engineering), where, even though the significance of uncertainty quantification motivates a Bayesian approach, there is no simple way to incorporate researcher intuition into the model. We validate our models by applying them to synthetic applications: a simple linear regression problem and two more complex structures based on partial differential equations. Finally, we review the advantages of our methodology, which include the simplicity of the implementation, the uncertainty reduction due to the added information and, in some occasions, the derivation of better point predictions, and we address limitations, mainly from the computational complexity perspective, such as the difficulty in choosing an appropriate algorithm and the added computational burden.

Highlight: This post can come as a very interesting and surprising one. You will see how we can apply a machine learning algorithm on the pixel intensity color with a so-called K-means clustering algorithm. In this way, we would be able to create a compressed version of our image that will have much fewer colors. The picture will be preserved in a lower color resolution, whereas the number of pixels will remain the same. This technique is very exciting, so we hope that you will enjoy it.

Linear algebra is to machine learning as flour to bakery: every machine learning model is based in linear algebra, as every cake is based in flour. It is not the only ingredient, of course. Machine learning models need vector calculus, probability, and optimization, as cakes need sugar, eggs, and butter. Applied machine learning, like bakery, is essentially about combining these mathematical ingredients in clever ways to create useful (tasty?) models. This document contains introductory level linear algebra notes for applied machine learning. It is meant as a reference rather than a comprehensive review. If you ever get confused by matrix multiplication, don't remember what was the $L_2$ norm, or the conditions for linear independence, this can serve as a quick reference. It also a good introduction for people that don't need a deep understanding of linear algebra, but still want to learn about the fundamentals to read about machine learning or to use pre-packaged machine learning ...

You want to know and to learn one of the top 10 most influencial algorithms of the 20th century? Then you are right in this course. We will cover many powerful techniques from the field of probabilistic programming. This field is fast-growing, because these technique are getting more and more famous and proof to be efficient and reliable. We will cover all major fields of Probabilistic Programming: Distributions, Markov Chain Monte Carlo, Gaussian Mixture Models, Bayesian Linear Regression, Bayesian Logistic Regression, and hidden Markov models.

The R-squared Goodness-of-Fit measure is one of the most widely available statistics accompanying the output of regression analysis in statistical software. Perhaps partially due to its widespread availability, it is also one of the most often misunderstood ones. In a regression with a single independent variable R2 is calculated as the ratio between the variation explained by the model and the total observed variation. It is often called the coefficient of determination and can be interpreted as the proportion of variation explained by the posed predictor. In such a case, it is equivalent to the square of the correlation coefficient of the observed and fitted values of the variable.

Created by Lazy Programmer Inc. Created by Lazy Programmer Inc. Support Vector Machines (SVM) are one of the most powerful machine learning models around, and this topic has been one that students have requested ever since I started making courses. These days, everyone seems to be talking about deep learning, but in fact there was a time when support vector machines were seen as superior to neural networks. One of the things you'll learn about in this course is that a support vector machine actually is a neural network, and they essentially look identical if you were to draw a diagram. The toughest obstacle to overcome when you're learning about support vector machines is that they are very theoretical. This theory very easily scares a lot of people away, and it might feel like learning about support vector machines is beyond your ability.

Several models have been developed to predict how the COVID-19 pandemic spreads, and how it could be contained with non-pharmaceutical interventions (NPIs) such as social distancing restrictions and school and business closures. This paper demonstrates how evolutionary AI could be used to facilitate the next step, i.e. determining most effective intervention strategies automatically. Through evolutionary surrogate-assisted prescription (ESP), it is possible to generate a large number of candidate strategies and evaluate them with predictive models. In principle, strategies can be customized for different countries and locales, and balance the need to contain the pandemic and the need to minimize their economic impact. While still limited by available data, early experiments suggest that workplace and school restrictions are the most important and need to be designed carefully. It also demonstrates that results of lifting restrictions can be unreliable, and suggests creative ways in which restrictions can be implemented softly, e.g. by alternating them over time. As more data becomes available, the approach can be increasingly useful in dealing with COVID-19 as well as possible future pandemics.