We propose Generative Well-intentioned Networks (GWINs), a novel framework for increasing the accuracy of certainty-based, closed-world classifiers. A conditional generative network recovers the distribution of observations that the classifier labels correctly with high certainty. We introduce a reject option to the classifier during inference, allowing the classifier to reject an observation instance rather than predict an uncertain label. These rejected observations are translated by the generative network to high-certainty representations, which are then relabeled by the classifier. This architecture allows for any certainty-based classifier or rejection function and is not limited to multilayer perceptrons. The capability of this framework is assessed using benchmark classification datasets and shows that GWINs significantly improve the accuracy of uncertain observations.

In the past decade, deep learning methods have seen tremendous success in various supervised and unsupervised learning tasks such as classification and generative modeling. More recently, deep neural networks have emerged in the domain of reinforcement learning as a tool to solve decision-making problems of unprecedented complexity, e.g., navigation problems or game-playing AI. Despite the successful combinations of ideas from quantum computing with machine learning methods, there have been relatively few attempts to design quantum algorithms that would enhance deep reinforcement learning. This is partly due to the fact that quantum enhancements of deep neural networks, in general, have not been as extensively investigated as other quantum machine learning methods. In contrast, projective simulation is a reinforcement learning model inspired by the stochastic evolution of physical systems that enables a quantum speed-up in decision making. In this paper, we develop a unifying framework that connects deep learning and projective simulation, opening the route to quantum improvements in deep reinforcement learning. Our approach is based on so-called generative energy-based models to design reinforcement learning methods with a computational advantage in solving complex and large-scale decision-making problems.

Logistic regression is a model for binary classification predictive modeling. The parameters of a logistic regression model can be estimated by the probabilistic framework called maximum likelihood estimation. Under this framework, a probability distribution for the target variable (class label) must be assumed and then a likelihood function defined that calculates the probability of observing the outcome given the input data and the model. This function can then be optimized to find the set of parameters that results in the largest sum likelihood over the training dataset. The maximum likelihood approach to fitting a logistic regression model both aids in better understanding the form of the logistic regression model and provides a template that can be used for fitting classification models more generally.

Probability is at the very core of a lot of data science algorithms. In fact, the solutions to so many data science problems are probabilistic in nature – hence I always advice focusing on learning statistics and probability before jumping into the algorithms. But I've seen a lot of aspiring data scientists shunning statistics, especially Bayesian statistics. It remains incomprehensible to a lot of analysts and data scientists. I'm sure a lot of you are nodding your head at this! Bayes' Theorem, a major aspect of Bayesian Statistics, was created by Thomas Bayes, a monk who lived during the eighteenth century. The very fact that we're still learning about it shows how influential his work has been across centuries!

Hyperparameter optimization for machine learning models is typically carried out by some sort of cross-validation procedure or global optimization, both of which require running the learning algorithm numerous times. We show that for Bayesian hierarchical models there is an appealing alternative that allows selecting good hyperparameters without learning the model parameters during the process at all, facilitated by the prior predictive distribution that marginalizes out the model parameters. We propose an approach that matches suitable statistics of the prior predictive distribution with ones provided by an expert and apply the general concept for matrix factorization models. For some Poisson matrix factorization models we can analytically obtain exact hyperparameters, including the number of factors, and for more complex models we propose a model-independent optimization procedure.

Model interpretation, or explanation of a machine learning classifier, aims to extract generalizable knowledge from a trained classifier into a human-understandable format, for various purposes such as model assessment, debugging and trust. From a computaional viewpoint, it is formulated as approximating the target classifier using a simpler interpretable model, such as rule models like a decision set/list/tree. Often, this approximation is handled as standard supervised learning and the only difference is that the labels are provided by the target classifier instead of ground truth. This paradigm is particularly popular because there exists a variety of well-studied supervised algorithms for learning an interpretable classifier. However, we argue that this paradigm is suboptimal for it does not utilize the unique property of the model interpretation problem, that is, the ability to generate synthetic instances and query the target classifier for their labels. We call this the active-query property, suggesting that we should consider model interpretation from an active learning perspective. Following this insight, we argue that the active-query property should be employed when designing a model interpretation algorithm, and that the generation of synthetic instances should be integrated seamlessly with the algorithm that learns the model interpretation. In this paper, we demonstrate that by doing so, it is possible to achieve more faithful interpretation with simpler model complexity. As a technical contribution, we present an active algorithm Active Decision Set Induction (ADS) to learn a decision set, a set of if-else rules, for model interpretation. ADS performs a local search over the space of all decision sets. In every iteration, ADS computes confidence intervals for the value of the objective function of all local actions and utilizes active-query to determine the best one.

Editor's note: James is a speaker for ODSC London this November! Be sure to check out his talk, "The How, Why, and When of Replacing Engineering Work with Compute Power" there. Deep learning has been made practical through modern computing power, but it is not the only technique benefiting from this large increase in power. Bayesian inference is up and coming technique whose recent progress is powered by the increase in computing power. We can explain the mathematical expression of Bayes formula using an example similar to the great Bayesian Methods for Hackers: Probabilistic Programming and Bayesian Inference to a financial context and using mathematical concepts intuitively arise from code.

Cross-entropy is commonly used in machine learning as a loss function. Cross-entropy is a measure from the field of information theory, building upon entropy and generally calculating the difference between two probability distributions. It is closely related to but is different from KL divergence that calculates the relative entropy between two probability distributions, whereas cross-entropy can be thought to calculate the total entropy between the distributions. Cross-entropy is also related to and often confused with logistic loss, called log loss. Although the two measures are derived from a different source, when used as loss functions for classification models, both measures calculate the same quantity and can be used interchangeably. In this tutorial, you will discover cross-entropy for machine learning.

Cross-entropy is commonly used in machine learning as a loss function. Cross-entropy is a measure from the field of information theory, building upon entropy and generally calculating the difference between two probability distributions. It is closely related to but is different from KL divergence that calculates the relative entropy between two probability distributions, whereas cross-entropy can be thought to calculate the total entropy between the distributions. Cross-entropy is also related to and often confused with logistic loss, called log loss. Although the two measures are derived from a different source, when used as loss functions for classification models, both measures calculate the same quantity and can be used interchangeably. In this tutorial, you will discover cross-entropy for machine learning.

Density estimation is the problem of estimating the probability distribution for a sample of observations from a problem domain. There are many techniques for solving density estimation, although a common framework used throughout the field of machine learning is maximum likelihood estimation. Maximum likelihood estimation involves defining a likelihood function for calculating the conditional probability of observing the data sample given a probability distribution and distribution parameters. This approach can be used to search a space of possible distributions and parameters. This flexible probabilistic framework also provides the foundation for many machine learning algorithms, including important methods such as linear regression and logistic regression for predicting numeric values and class labels respectively, but also more generally for deep learning artificial neural networks.