Probability is a field of mathematics that is universally agreed to be the bedrock for machine learning. Although probability is a large field with many esoteric theories and findings, the nuts and bolts, tools and notations taken from the field are required for machine learning practitioners. With a solid foundation of what probability is, it is possible to focus on just the good or relevant parts. In this crash course, you will discover how you can get started and confidently understand and implement probabilistic methods used in machine learning with Python in seven days. This is a big and important post. You might want to bookmark it. Probability for Machine Learning (7-Day Mini-Course) Photo by Percita, some rights reserved.

This book was designed around major ideas and methods that are directly relevant to machine learning algorithms. There are a lot of things you could learn about probability, from theory to abstract concepts to APIs. My goal is to take you straight to developing an intuition for the elements you must understand with laser-focused tutorials. I designed the tutorials to focus on how to get things done with probability. They give you the tools to both rapidly understand and apply each technique or operation. Each tutorial is designed to take you less than one hour to read through and complete, excluding the extensions and further reading. You can choose to work through the lessons one per day, one per week, or at your own pace. I think momentum is critically important, and this book is intended to be read and used, not to sit idle. I would recommend picking a schedule and sticking to it.

Business favors decisive action and leadership, so learning to embrace uncertainty as a good thing could be difficult. If you're a business leader hoping to implement AI into your operations in the next few months or years, you're going to have to make peace with that word. Here's why uncertainty in AI is good for business. Like many things, uncertainty has a different intention in the science field than it does in popular usage. When we're talking about learning models, we're trying to use the concept of uncertainty to allow models to learn more like humans and make fewer mistakes as a result.

In this study, a hybrid method based on an Adaptive Neuro-Fuzzy Inference System (ANFIS) and Particle Swarm Optimization (PSO) for diagnosing Liver disorders (ANFIS-PSO) is introduced. This smart diagnosis method deals with a combination of making an inference system and optimization process which tries to tune the hyper-parameters of ANFIS based on the data-set. The Liver diseases characteristics are taken from the UCI Repository of Machine Learning Databases. The number of these characteristic attributes are 7, and the sample number is 354. The right diagnosis performance of the ANFIS-PSO intelligent medical system for liver disease is evaluated by using classification accuracy, sensitivity and specificity analysis, respectively. According to the experimental results, the performance of ANFIS-PSO can be more considerable than traditional FIS and ANFIS without optimization phase.

We introduce the Mutual Information Machine (MIM), a novel formulation of representation learning, using a joint distribution over the observations and latent state in an encoder/decoder framework. Our key principles are symmetry and mutual information, where symmetry encourages the encoder and decoder to learn different factorizations of the same underlying distribution, and mutual information, to encourage the learning of useful representations for downstream tasks. Our starting point is the symmetric Jensen-Shannon divergence between the encoding and decoding joint distributions, plus a mutual information encouraging regularizer. We show that this can be bounded by a tractable cross entropy loss function between the true model and a parameterized approximation, and relate this to the maximum likelihood framework. We also relate MIM to variational autoencoders (VAEs) and demonstrate that MIM is capable of learning symmetric factorizations, with high mutual information that avoids posterior collapse.

To understand how rich dynamics emerge in neural populations, we require models which exhibit a wide range of dynamics while remaining interpretable in terms of connectivity and single-neuron dynamics. However, it has been challenging to fit such mechanistic spiking networks at the single neuron scale to empirical population data. To close this gap, we propose to fit such data at a meso scale, using a mechanistic but low-dimensional and hence statistically tractable model. The mesoscopic representation is obtained by approximating a population of neurons as multiple homogeneous `pools' of neurons, and modelling the dynamics of the aggregate population activity within each pool. We derive the likelihood of both single-neuron and connectivity parameters given this activity, which can then be used to either optimize parameters by gradient ascent on the log-likelihood, or to perform Bayesian inference using Markov Chain Monte Carlo (MCMC) sampling. We illustrate this approach using a model of generalized integrate-and-fire neurons for which mesoscopic dynamics have been previously derived, and show that both single-neuron and connectivity parameters can be recovered from simulated data. In particular, our inference method extracts posterior correlations between model parameters, which define parameter subsets able to reproduce the data. We compute the Bayesian posterior for combinations of parameters using MCMC sampling and investigate how the approximations inherent to a mesoscopic population model impact the accuracy of the inferred single-neuron parameters.

Meta-learning over a set of distributions can be interpreted as learning different types of parameters corresponding to short-term vs long-term aspects of the mechanisms underlying the generation of data. These are respectively captured by quickly-changing parameters and slowly-changing meta-parameters. We present a new framework for meta-learning causal models where the relationship between each variable and its parents is modeled by a neural network, modulated by structural meta-parameters which capture the overall topology of a directed graphical model. Our approach avoids a discrete search over models in favour of a continuous optimization procedure. We study a setting where interventional distributions are induced as a result of a random intervention on a single unknown variable of an unknown ground truth causal model, and the observations arising after such an intervention constitute one meta-example. To disentangle the slow-changing aspects of each conditional from the fast-changing adaptations to each intervention, we parametrize the neural network into fast parameters and slow meta-parameters. We introduce a meta-learning objective that favours solutions robust to frequent but sparse interventional distribution change, and which generalize well to previously unseen interventions. Optimizing this objective is shown experimentally to recover the structure of the causal graph.

Spiking neural networks (SNNs) are distributed trainable systems whose computing elements, or neurons, are characterized by internal analog dynamics and by digital and sparse synaptic communications. The sparsity of the synaptic spiking inputs and the corresponding event-driven nature of neural processing can be leveraged by energy-efficient hardware implementations, which can offer significant energy reductions as compared to conventional artificial neural networks (ANNs). The design of training algorithms lags behind the hardware implementations. Most existing training algorithms for SNNs have been designed either for biological plausibility or through conversion from pretrained ANNs via rate encoding. This article provides an introduction to SNNs by focusing on a probabilistic signal processing methodology that enables the direct derivation of learning rules by leveraging the unique time-encoding capabilities of SNNs. We adopt discrete-time probabilistic models for networked spiking neurons and derive supervised and unsupervised learning rules from first principles via variational inference. Examples and open research problems are also provided.

By exploiting mini-batch stochastic gradient optimisation, variational inference has had great success in scaling up approximate Bayesian inference to big data. To date, however, this strategy has only been applicable to models of independent data. Here we extend mini-batch variational methods to state space models of time series data. To do so we introduce a novel generative model as our variational approximation, a local inverse autoregressive flow. This allows a subsequence to be sampled without sampling the entire distribution. Hence we can perform training iterations using short portions of the time series at low computational cost. We illustrate our method on AR(1), Lotka-Volterra and FitzHugh-Nagumo models, achieving accurate parameter estimation in a short time.