We develop a privatised stochastic variational inference method for Latent Dirichlet Allocation (LDA). The iterative nature of stochastic variational inference presents challenges: multiple iterations are required to obtain accurate posterior distributions, yet each iteration increases the amount of noise that must be added to achieve a reasonable degree of privacy. We propose a practical algorithm that overcomes this challenge by combining: (1) A relaxed notion of the differential privacy, called concentrated differential privacy, which provides high probability bounds for cumulative privacy loss, which is well suited for iterative algorithms, rather than focusing on single-query loss; and (2) Privacy amplification resulting from subsampling of large-scale data. Focusing on conjugate exponential family models, in our private variational inference, all the posterior distributions will be privatised by simply perturbing expected sufficient statistics. Using Wikipedia data, we illustrate the effectiveness of our algorithm for large-scale data.

Recent progress implies that a crossover between machine learning and quantum information processing benefits both fields. Traditional machine learning has dramatically improved the benchmarking and control of experimental quantum computing systems, including adaptive quantum phase estimation and designing quantum computing gates. On the other hand, quantum mechanics offers tantalizing prospects to enhance machine learning, ranging from reduced computational complexity to improved generalization performance. The most notable examples include quantum enhanced algorithms for principal component analysis, quantum support vector machines, and quantum Boltzmann machines. Progress has been rapid, fostered by demonstrations of midsized quantum optimizers which are predicted to soon outperform their classical counterparts. Further, we are witnessing the emergence of a physical theory pinpointing the fundamental and natural limitations of learning. Here we survey the cutting edge of this merger and list several open problems.

Relational learning deals with data that are characterized by relational structures. An important task is collective classification, which is to jointly classify networked objects. While it holds a great promise to produce a better accuracy than non-collective classifiers, collective classification is computational challenging and has not leveraged on the recent breakthroughs of deep learning. We present Column Network (CLN), a novel deep learning model for collective classification in multi-relational domains. CLN has many desirable theoretical properties: (i) it encodes multi-relations between any two instances; (ii) it is deep and compact, allowing complex functions to be approximated at the network level with a small set of free parameters; (iii) local and relational features are learned simultaneously; (iv) long-range, higher-order dependencies between instances are supported naturally; and (v) crucially, learning and inference are efficient, linear in the size of the network and the number of relations. We evaluate CLN on multiple real-world applications: (a) delay prediction in software projects, (b) PubMed Diabetes publication classification and (c) film genre classification. In all applications, CLN demonstrates a higher accuracy than state-of-the-art rivals.

This work investigates the case of a network of agents that attempt to learn some unknown state of the world amongst the finitely many possibilities. At each time step, agents all receive random, independently distributed private signals whose distributions are dependent on the unknown state of the world. However, it may be the case that some or any of the agents cannot distinguish between two or more of the possible states based only on their private observations, as when several states result in the same distribution of the private signals. In our model, the agents form some initial belief (probability distribution) about the unknown state and then refine their beliefs in accordance with their private observations, as well as the beliefs of their neighbors. An agent learns the unknown state when her belief converges to a point mass that is concentrated at the true state. A rational agent would use the Bayes' rule to incorporate her neighbors' beliefs and own private signals over time. While such repeated applications of the Bayes' rule in networks can become computationally intractable, in this paper, we show that in the canonical cases of directed star, circle or path networks and their combinations, one can derive a class of memoryless update rules that replicate that of a single Bayesian agent but replace the self beliefs with the beliefs of the neighbors. This way, one can realize an exponentially fast rate of learning similar to the case of Bayesian (fully rational) agents. The proposed rules are a special case of the Learning without Recall.

Functional MRI (fMRI) and diffusion MRI (dMRI) are non-invasive imaging modalities that allow in-vivo analysis of a patient's brain network (known as a connectome). Use of these technologies has enabled faster and better diagnoses and treatments of neurological disorders and a deeper understanding of the human brain. Recently, researchers have been exploring the application of machine learning models to connectome data in order to predict clinical outcomes and analyze the importance of subnetworks in the brain. Connectome data has unique properties, which present both special challenges and opportunities when used for machine learning. The purpose of this work is to review the literature on the topic of applying machine learning models to MRI-based connectome data. This field is growing rapidly and now encompasses a large body of research. To summarize the research done to date, we provide a comparative, structured summary of 77 relevant works, tabulated according to different criteria, that represent the majority of the literature on this topic. (We also published a living version of this table online at http://connectomelearning.cs.sfu.ca that the community can continue to contribute to.) After giving an overview of how connectomes are constructed from dMRI and fMRI data, we discuss the variety of machine learning tasks that have been explored with connectome data. We then compare the advantages and drawbacks of different machine learning approaches that have been employed, discussing different feature selection and feature extraction schemes, as well as the learning models and regularization penalties themselves. Throughout this discussion, we focus particularly on how the methods are adapted to the unique nature of graphical connectome data. Finally, we conclude by summarizing the current state of the art and by outlining what we believe are strategic directions for future research.

Developed back in the 50s by Rosenblatt and colleagues, this extremely simple algorithm can be viewed as the foundation for some of the most successful classifiers today, including suport vector machines and logistic regression, solved using stochastic gradient descent. The convergence proof for the Perceptron algorithm is one of the most elegant pieces of math I've seen in ML. Most useful: Boosting, especially boosted decision trees. This intuitive approach allows you to build highly accurate ML models, by combining many simple ones. Boosting is one of the most practical methods in ML, it's widely used in industry, can handle a wide variety of data types, and can be implemented at scale.

Various active learning methods based on logistic regression have been proposed. In this paper, we investigate seven state-of-the-art strategies, present an extensive benchmark, and provide a better understanding of their underlying characteristics. Experiments are carried out both on 3 synthetic datasets and 43 real-world datasets, providing insights into the behaviour of these active learning methods with respect to classification accuracy and their computational cost.

Since about 100 years ago, to learn the intrinsic structure of data, many representation learning approaches have been proposed, including both linear ones and nonlinear ones, supervised ones and unsupervised ones. Particularly, deep architectures are widely applied for representation learning in recent years, and have delivered top results in many tasks, such as image classification, object detection and speech recognition. In this paper, we review the development of data representation learning methods. Specifically, we investigate both traditional feature learning algorithms and state-of-the-art deep learning models. The history of data representation learning is introduced, while available resources (e.g. online course, tutorial and book information) and toolboxes are provided. Finally, we conclude this paper with remarks and some interesting research directions on data representation learning.

Markov logic networks (MLNs) reconcile two opposing schools in machine learning and artificial intelligence: causal networks, which account for uncertainty extremely well, and first-order logic, which allows for formal deduction. An MLN is essentially a first-order logic template to generate Markov networks. Inference in MLNs is probabilistic and it is often performed by approximate methods such as Markov chain Monte Carlo (MCMC) Gibbs sampling. An MLN has many regular, symmetric structures that can be exploited at both first-order level and in the generated Markov network. We analyze the graph structures that are produced by various lifting methods and investigate the extent to which quantum protocols can be used to speed up Gibbs sampling with state preparation and measurement schemes. We review different such approaches, discuss their advantages, theoretical limitations, and their appeal to implementations. We find that a straightforward application of a recent result yields exponential speedup compared to classical heuristics in approximate probabilistic inference, thereby demonstrating another example where advanced quantum resources can potentially prove useful in machine learning.

After researching and looking into the different algorithms associated with Machine Learning, I've found that there is an abundance of great material showing you how to use certain algorithms in a specific language. However what's usually missing is the simple mathematical explaination of how the algorithm works. In all cases this may not be possible without a strong mathematical background, but for some I know I would definitely find it useful. This post requires just basic mathematics knowledge and an interst in data science and machine learning. I will be talking about Naive Bayes as a classifier and explaining in simple terms how it works and when you might use it.