Bayesian optimization (\bo) is a global optimization strategy designed to find the minimum of an expensive black-box function, typically defined on a continuous subset of $\mathcal{R}^d$, by using a Gaussian process (\gp) as a surrogate model for the objective. Although currently available acquisition functions address this goal with different degree of success, an over-exploration effect of the contour of the search space is typically observed. However, in problems like the configuration of machine learning algorithms, the function domain is conservatively large and with a high probability the global minimum does not sit the boundary. We propose a method to incorporate this knowledge into the searching process by adding virtual derivative observations in the \gp at the borders of the search space. We use the properties of \gps to impose conditions on the partial derivatives of the objective. The method is applicable with any acquisition function, it is easy to use and consistently reduces the number of evaluations required to optimize the objective irrespective of the acquisition used. We illustrate the benefits our approach in an extensive experimental comparison.

Graphs are a prevalent tool in data science, as they model the inherent structure of the data. They have been used successfully in unsupervised and semi-supervised learning. Typically they are constructed either by connecting nearest samples, or by learning them from data, solving an optimization problem. While graph learning does achieve a better quality, it also comes with a higher computational cost. In particular, the current state-of-the-art model cost is $\mathcal{O}(n^2)$ for $n$ samples. In this paper, we show how to scale it, obtaining an approximation with leading cost of $\mathcal{O}(n\log(n))$, with quality that approaches the exact graph learning model. Our algorithm uses known approximate nearest neighbor techniques to reduce the number of variables, and automatically selects the correct parameters of the model, requiring a single intuitive input: the desired edge density.

But how can we train graphical models on a massive data set? In this paper, we show how to construct coresets--compressed data sets which can be used as proxy for the original data and have provably bounded worst case error--for Gaussian dependency networks (DNs), i.e., cyclic directed graphical models over Gaussians, where the parents of each variable are its Markov blanket. Specifically, we prove that Gaussian DNs admit coresets of size independent of the size of the data set. Unfortunately, this does not extend to DNs over members of the exponential family in general. As we will prove, Poisson DNs do not admit small coresets. Despite this worst-case result, we will provide an argument why our coreset construction for DNs can still work well in practice on count data. To corroborate our theoretical results, we empirically evaluated the resulting Core DNs on real data sets. The results demonstrate significant gains over no or naive sub-sampling, even in the case of count data.

In this paper, we propose a novel ranking framework for collaborative filtering with the overall aim of learning user preferences over items by minimizing a pairwise ranking loss. We show the minimization problem involves dependent random variables and provide a theoretical analysis by proving the consistency of the empirical risk minimization in the worst case where all users choose a minimal number of positive and negative items. We further derive a Neural-Network model that jointly learns a new representation of users and items in an embedded space as well as the preference relation of users over the pairs of items. The learning objective is based on three scenarios of ranking losses that control the ability of the model to maintain the ordering over the items induced from the users' preferences, as well as, the capacity of the dot-product defined in the learned embedded space to produce the ordering. The proposed model is by nature suitable for implicit feedback and involves the estimation of only very few parameters. Through extensive experiments on several real-world benchmarks on implicit data, we show the interest of learning the preference and the embedding simultaneously when compared to learning those separately. We also demonstrate that our approach is very competitive with the best state-of-the-art collaborative filtering techniques proposed for implicit feedback.

Given data over the joint distribution of two random variables $X$ and $Y$, we consider the problem of inferring the most likely causal direction between $X$ and $Y$. In particular, we consider the general case where both $X$ and $Y$ may be univariate or multivariate, and of the same or mixed data types. We take an information theoretic approach, based on Kolmogorov complexity, from which it follows that first describing the data over cause and then that of effect given cause is shorter than the reverse direction. The ideal score is not computable, but can be approximated through the Minimum Description Length (MDL) principle. Based on MDL, we propose two scores, one for when both $X$ and $Y$ are of the same single data type, and one for when they are mixed-type. We model dependencies between $X$ and $Y$ using classification and regression trees. As inferring the optimal model is NP-hard, we propose Crack, a fast greedy algorithm to determine the most likely causal direction directly from the data. Empirical evaluation on a wide range of data shows that Crack reliably, and with high accuracy, infers the correct causal direction on both univariate and multivariate cause-effect pairs over both single and mixed-type data.

Quantum annealers aim at solving non-convex optimization problems by exploiting cooperative tunneling effects to escape local minima. The underlying idea consists in designing a classical energy function whose ground states are the sought optimal solutions of the original optimization problem and add a controllable quantum transverse field to generate tunneling processes. A key challenge is to identify classes of non-convex optimization problems for which quantum annealing remains efficient while thermal annealing fails. We show that this happens for a wide class of problems which are central to machine learning. Their energy landscapes is dominated by local minima that cause exponential slow down of classical thermal annealers while simulated quantum annealing converges efficiently to rare dense regions of optimal solutions.

Comprehending complex systems by simplifying and highlighting important dynamical patterns requires modeling and mapping higher-order network flows. However, complex systems come in many forms and demand a range of representations, including memory and multilayer networks, which in turn call for versatile community-detection algorithms to reveal important modular regularities in the flows. Here we show that various forms of higher-order network flows can be represented in a unified way with networks that distinguish physical nodes for representing a~complex system's objects from state nodes for describing flows between the objects. Moreover, these so-called sparse memory networks allow the information-theoretic community detection method known as the map equation to identify overlapping and nested flow modules in data from a range of~different higher-order interactions such as multistep, multi-source, and temporal data. We derive the map equation applied to sparse memory networks and describe its search algorithm Infomap, which can exploit the flexibility of sparse memory networks. Together they provide a general solution to reveal overlapping modular patterns in higher-order flows through complex systems.

Forecasting financial time series using past observations has been a topic of significant interest for obvious reasons. It is well known that while temporal relationships in the data exist, they are difficult to analyze and predict accurately due to the nonlinear trends and noise present in the series. In developing models for forecasting financial data it is desirable that these will be both able to learn nonlinear dependencies in the data as well as have a high noise resistance. Feedforward neural networks have been a popular way of learning the dependencies in the data, by e.g. using multiple inputs from the past to make a prediction for the future time step, see [3]. One downside of classical feedforward neural networks is that a large sample size of data is required to obtain a stable forecasting result. The main focus of this paper is on multivariate time series forecasting, specifically financial time series. In particular, we forecast time series conditional on other, related series.

We've built a global partnership network with top universities such as MIT, Stanford, NYU, and the University of Amsterdam to explore the future of machine learning and advance the technology for business. Through this collaboration, we focus on a variety of machine learning research topics – and work on solving open AI challenges in a range of industries. This large pool of expertise helps us keep pace with the latest machine learning trends and deliver new techniques in the context of SAP solutions.

Can artificial intelligence replace the human brain?Will it? "Humans were are not built to spend more than two hours looking at a screen or scrolling through excel sheets. Humans are best at being human. Artificial Intelligence will do the rest." Kind of an employment company run by three humans overseeing 59 robots (actually computers working on algorithms created at the University of Amsterdam to solve problems).