It seems like machine learning and artificial intelligence are topics at the top of everyone's mind in tech. Be it autonomous cars, robots, or machine intelligence in general, everyone's talking about machines getting smarter and being able to do more. At the same time, for many developers, machine learning and artificial intelligence are nebulous terms representing complex mathematical and data problems they just don't have the time to explore and learn. As I've spoken with lots of developers and CTOs about Fuzzy.io and our mission to make it easy for developers to start bringing intelligent decision-making to their software without needing huge amounts of data or AI expertise, some were curious to learn more about the greater landscape of machine learning. Here are some of the links to articles, podcasts and courses discussing some of the basics of machine learning that I've shared with them.

In this paper we introduce a novel framework for making exact nonparametric Bayesian inference on latent functions, that is particularly suitable for Big Data tasks. Firstly, we introduce a class of stochastic processes we refer to as string Gaussian processes (string GPs), which are not to be mistaken for Gaussian processes operating on text. We construct string GPs so that their finite-dimensional marginals exhibit suitable local conditional independence structures, which allow for scalable, distributed, and flexible nonparametric Bayesian inference, without resorting to approximations, and while ensuring some mild global regularity constraints. Furthermore, string GP priors naturally cope with heterogeneous input data, and the gradient of the learned latent function is readily available for explanatory analysis. Secondly, we provide some theoretical results relating our approach to the standard GP paradigm. In particular, we prove that some string GPs are Gaussian processes, which provides a complementary global perspective on our framework. Finally, we derive a scalable and distributed MCMC scheme for supervised learning tasks under string GP priors. The proposed MCMC scheme has computational time complexity $\mathcal{O}(N)$ and memory requirement $\mathcal{O}(dN)$, where $N$ is the data size and $d$ the dimension of the input space. We illustrate the efficacy of the proposed approach on several synthetic and real-world datasets, including a dataset with $6$ millions input points and $8$ attributes.

It is no doubt that the sub-field of machine learning / artificial intelligence has increasingly gained more popularity in the past couple of years. As Big Data is the hottest trend in the tech industry at the moment, machine learning is incredibly powerful to make predictions or calculated suggestions based on large amounts of data. Some of the most common examples of machine learning are Netflix's algorithms to make movie suggestions based on movies you have watched in the past or Amazon's algorithms that recommend books based on books you have bought before. So if you want to learn more about machine learning, how do you start? For me, my first introduction is when I took an Artificial Intelligence class when I was studying abroad in Copenhagen. My lecturer is a full-time Applied Math and CS professor at the Technical University of Denmark, in which his research areas are logic and artificial, focusing primarily on the use of logic to model human-like planning, reasoning and problem solving.

So you know the Bayes rule. How does it relate to machine learning? It can be quite difficult to grasp how the puzzle pieces fit together - we know it took us a while. This article is an introduction we wish we had back then. While we have some grasp on the matter, we're not experts, so the following might contain inaccuracies or even outright errors. Feel free to point them out, either in the comments or privately.

Probabilistic techniques are central to data analysis, but different approaches can be difficult to apply, combine, and compare. This paper introduces composable generative population models (CGPMs), a computational abstraction that extends directed graphical models and can be used to describe and compose a broad class of probabilistic data analysis techniques. Examples include hierarchical Bayesian models, multivariate kernel methods, discriminative machine learning, clustering algorithms, dimensionality reduction, and arbitrary probabilistic programs. We also demonstrate the integration of CGPMs into BayesDB, a probabilistic programming platform that can express data analysis tasks using a modeling language and a structured query language. The practical value is illustrated in two ways. First, CGPMs are used in an analysis that identifies satellite data records which probably violate Kepler's Third Law, by composing causal probabilistic programs with non-parametric Bayes in under 50 lines of probabilistic code. Second, for several representative data analysis tasks, we report on lines of code and accuracy measurements of various CGPMs, plus comparisons with standard baseline solutions from Python and MATLAB libraries.

We consider log-supermodular models on binary variables, which are probabilistic models with negative log-densities which are submodular. These models provide probabilistic interpretations of common combinatorial optimization tasks such as image segmentation. In this paper, we focus primarily on parameter estimation in the models from known upper-bounds on the intractable log-partition function. We show that the bound based on separable optimization on the base polytope of the submodular function is always inferior to a bound based on "perturb-and-MAP" ideas. Then, to learn parameters, given that our approximation of the log-partition function is an expectation (over our own randomization), we use a stochastic subgradient technique to maximize a lower-bound on the log-likelihood. This can also be extended to conditional maximum likelihood. We illustrate our new results in a set of experiments in binary image denoising, where we highlight the flexibility of a probabilistic model to learn with missing data.

However, the idea of building a generative model via an energy function is a good one. Since it is a probabilistic model, training a Boltzmann Machine often involves maximizing its likelihood function, which is proportional to the energy divided by the total energy of all configurations. This total energy is formally called the partition function, and is generally intractable. By restricting the connections of a Boltzmann Machine to be bipartite, people came up with Restricted Boltzmann Machine (RBM), whose inference can be approximated by MCMC and similar methods. Using RBMs to pre-train a deep feedforward nets is one of the main breakthroughs in Deep Learning several years ago.

Rich and complex time-series data, such as those generated from engineering systems, financial markets, videos or neural recordings, are now a common feature of modern data analysis. Explaining the phenomena underlying these diverse data sets requires flexible and accurate models. In this paper, we promote Gaussian process dynamical systems (GPDS) as a rich model class that is appropriate for such analysis. In particular, we present a message passing algorithm for approximate inference in GPDSs based on expectation propagation. By posing inference as a general message passing problem, we iterate forward-backward smoothing. Thus, we obtain more accurate posterior distributions over latent structures, resulting in improved predictive performance compared to state-of-the-art GPDS smoothers, which are special cases of our general message passing algorithm. Hence, we provide a unifying approach within which to contextualize message passing in GPDSs.

Crop yield forecasting is the methodology of predicting crop yields prior to harvest. The availability of accurate yield prediction frameworks have enormous implications from multiple standpoints, including impact on the crop commodity futures markets, formulation of agricultural policy, as well as crop insurance rating. The focus of this work is to construct a corn yield predictor at the county scale. Corn yield (forecasting) depends on a complex, interconnected set of variables that include economic, agricultural, management and meteorological factors. Conventional forecasting is either knowledge-based computer programs (that simulate plant-weather-soil-management interactions) coupled with targeted surveys or statistical model based. The former is limited by the need for painstaking calibration, while the latter is limited to univariate analysis or similar simplifying assumptions that fail to capture the complex interdependencies affecting yield. In this paper, we propose a data-driven approach that is "gray box" i.e. that seamlessly utilizes expert knowledge in constructing a statistical network model for corn yield forecasting. Our multivariate gray box model is developed on Bayesian network analysis to build a Directed Acyclic Graph (DAG) between predictors and yield. Starting from a complete graph connecting various carefully chosen variables and yield, expert knowledge is used to prune or strengthen edges connecting variables. Subsequently the structure (connectivity and edge weights) of the DAG that maximizes the likelihood of observing the training data is identified via optimization. We curated an extensive set of historical data (1948-2012) for each of the 99 counties in Iowa as data to train the model.

Determinantal point processes (DPPs) are an elegant model for encoding probabilities over subsets, such as shopping baskets, of a ground set, such as an item catalog. They are useful for a number of machine learning tasks, including product recommendation. DPPs are parametrized by a positive semi-definite kernel matrix. Recent work has shown that using a low-rank factorization of this kernel provides remarkable scalability improvements that open the door to training on large-scale datasets and computing online recommendations, both of which are infeasible with standard DPP models that use a full-rank kernel. In this paper we present a low-rank DPP mixture model that allows us to represent the latent structure present in observed subsets as a mixture of a number of component low-rank DPPs, where each component DPP is responsible for representing a portion of the observed data. The mixture model allows us to effectively address the capacity constraints of the low-rank DPP model. We present an efficient and scalable Markov Chain Monte Carlo (MCMC) learning algorithm for our model that uses Gibbs sampling and stochastic gradient Hamiltonian Monte Carlo (SGHMC). Using an evaluation on several real-world product recommendation datasets, we show that our low-rank DPP mixture model provides substantially better predictive performance than is possible with a single low-rank or full-rank DPP, and significantly better performance than several other competing recommendation methods in many cases.