There can be one or many solutions to a given problem, depending on the scenario, As there can be many ways to solve that problem. Think about how do you approach a problem. Lets say you need to do something straight forward like a math multiplication. Clearly there is one correct solution, but many algorithms to multiply, depending on the size of the input. Now, take a more complicated problem, like playing a game(imagine your favorite game, chess, poker, call of duty, DOTA, anything..).

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.

We present a noise-injected version of the Expectation-Maximization (EM) algorithm: the Noisy Expectation Maximization (NEM) algorithm. The NEM algorithm uses noise to speed up the convergence of the EM algorithm. The NEM theorem shows that injected noise speeds up the average convergence of the EM algorithm to a local maximum of the likelihood surface if a positivity condition holds. The generalized form of the noisy expectation-maximization (NEM) algorithm allow for arbitrary modes of noise injection including adding and multiplying noise to the data. We demonstrate these noise benefits on EM algorithms for the Gaussian mixture model (GMM) with both additive and multiplicative NEM noise injection. A separate theorem (not presented here) shows that the noise benefit for independent identically distributed additive noise decreases with sample size in mixture models. This theorem implies that the noise benefit is most pronounced if the data is sparse. Injecting blind noise only slowed convergence.

We propose novel semi-supervised and active learning algorithms for the problem of community detection on networks. The algorithms are based on optimizing the likelihood function of the community assignments given a graph and an estimate of the statistical model that generated it. The optimization framework is inspired by prior work on the unsupervised community detection problem in Stochastic Block Models (SBM) using Semi-Definite Programming (SDP). In this paper we provide the next steps in the evolution of learning communities in this context which involves a constrained semi-definite programming algorithm, and a newly presented active learning algorithm. The active learner intelligently queries nodes that are expected to maximize the change in the model likelihood. Experimental results show that this active learning algorithm outperforms the random-selection semi-supervised version of the same algorithm as well as other state-of-the-art active learning algorithms. Our algorithms significantly improved performance is demonstrated on both real-world and SBM-generated networks even when the SBM has a signal to noise ratio (SNR) below the known unsupervised detectability threshold.

With the emergence of connected devices (e.g., smartphones and smartmeters), pervasive systems generate growing amounts of digital traces as users undergo their everyday activities. These traces are crucial to service providers to understand their customers, to increase the degree of personalization, and enhance the quality of their services. For instance, personal digital traces stemming from public transit smartcards help transportation providers understand the commuting patterns of users; the usage statistics of home appliances can be used to improve energy efficiency; on-street cameras provide police officers with new ways of investigating crimes; content generated through mobile and wearables (such as posts in online social media or GPS running routes in specialized websites such as those for fitness) can be used to provide tailored content to individuals; bank transaction logs can be used to spot unusual activity in accounts. However, sharing these digital traces generated by pervasive systems with service providers might raise concerns with regards to privacy. Indeed, the processing and analysis of these digital traces can surface latent information about the behavior of the users. While service providers have to store the usergenerated data in large databases that guarantee a certain level of privacy (e.g., from storing the traces in an anonymized manner using randomly-generated identifiers instead of the real user's name and surname to using more sophisticated privacy-preserving techniques such as differential privacy), third parties such as advertisers that have access to the traces can leverage machine learning techniques to reveal personal information about the users and expose their privacy [1]. This includes inferring personal information about users and identifying a single individual from a collection of user-generated traces. Moreover, these traces might reveal information about the significant places routinely visited by the user, enabling the service provider to infer a wide range of personal information, including the user's place of residence and work and their future locations. To a further extent, presence traces can also be used to identify a specific individual in a population.

We consider the problem of sampling from a strongly log-concave density in $\mathbb{R}^d$, and prove a non-asymptotic upper bound on the mixing time of the Metropolis-adjusted Langevin algorithm (MALA). The method draws samples by running a Markov chain obtained from the discretization of an appropriate Langevin diffusion, combined with an accept-reject step to ensure the correct stationary distribution. Relative to known guarantees for the unadjusted Langevin algorithm (ULA), our bounds show that the use of an accept-reject step in MALA leads to an exponentially improved dependence on the error-tolerance. Concretely, in order to obtain samples with TV error at most $\delta$ for a density with condition number $\kappa$, we show that MALA requires $\mathcal{O} \big(\kappa d \log(1/\delta) \big)$ steps, as compared to the $\mathcal{O} \big(\kappa^2 d/\delta^2 \big)$ steps established in past work on ULA. We also demonstrate the gains of MALA over ULA for weakly log-concave densities. Furthermore, we derive mixing time bounds for a zeroth-order method Metropolized random walk (MRW) and show that it mixes $\mathcal{O}(\kappa d)$ slower than MALA. We provide numerical examples that support our theoretical findings, and demonstrate the potential gains of Metropolis-Hastings adjustment for Langevin-type algorithms.

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.

About this course: Bayesian methods are used in lots of fields: from game development to drug discovery. They give superpowers to many machine learning algorithms: handling missing data, extracting much more information from small datasets. Bayesian methods also allow us to estimate uncertainty in predictions, which is a really desirable feature for fields like medicine. When Bayesian methods are applied to deep learning, it turns out that they allow you to compress your models 100 folds, and automatically tune hyperparametrs, saving your time and money. In six weeks we will discuss the basics of Bayesian methods: from how to define a probabilistic model to how to make predictions from it.

In this post I'll explain what the maximum likelihood method for parameter estimation is and go through a simple example to demonstrate the method. Some of the content requires knowledge of fundamental probability concepts such as the definition of joint probability and independence of events. I've written a blog post with these prerequisites so feel free to read this if you think you need a refresher. Often in machine learning we use a model to describe the process that results in the data that are observed. For example, we may use a random forest model to classify whether customers may cancel a subscription from a service (known as churn modelling) or we may use a linear model to predict the revenue that will be generated for a company depending on how much they may spend on advertising (this would be an example of linear regression).

Classification and clustering for samples of event time data using non-homogeneous Poisson process models Duncan S Barrack a and Simon Preston b a Horizon Digital Economy Research Institute, University of Nottingham, Nottingham, UK. b School of Mathematical Sciences, University of Nottingham, Nottingham, UK. Abstract Data of the form of event times arise in various applications. A simple model for such data is a non-homogeneous Poisson process (NHPP) which is specified by a rate function that depends on time. We consider the problem of having access to multiple independent samples of event time data, observed on a common interval, from which we wish to classify or cluster the samples according to their rate functions. Each rate function is unknown but assumed to belong to a finite number of rate functions each defining a distinct class. We model the rate functions using a spline basis expansion, the coefficients of which need to be estimated from data. The classification approach consists of using training data for which the class membership is known, to calculate maximum likelihood estimates of the coefficients for each group, then assigning test samples to a class by a maximum likelihood criterion. For clustering, by analogy to the Gaussian mixture model approach for Euclidean data, we consider a mixture of NHPP models and use the expectation-maximisation algorithm to estimate the coefficients of the rate functions for the component models and cluster membership probabilities for each sample. The classification and clustering approaches perform well on both synthetic and real-world data sets.