These and other findings are from the McKinsey Global Institute Study, and discussion paper, Artificial Intelligence, The Next Digital Frontier (80 pp., PDF, free, no opt-in) published last month. McKinsey Global Institute published an article summarizing the findings titled How Artificial Intelligence Can Deliver Real Value To Companies. McKinsey interviewed more than 3,000 senior executives on the use of AI technologies, their companies' prospects for further deployment, and AI's impact on markets, governments, and individuals. McKinsey Analytics was also utilized in the development of this study and discussion paper.

The Ornstein-Uhlenbeck, also called mean-reverting diffusion process, describes a process which evolves following a deterministic linear part with an added Gaussian noise, similarly to a vectorautoregressive process in discrete time. This model is ubiquitous in quantitative finance, for instance the one-dimensional version is used for modeling rates and is called the Vasicek model [Hul09]. In a multidimensional setting, it can be therefore used to describe systems with linear interactions perturbed by Gaussian noise, see Figure 1 below. Among many others, an example of application is inter-bank lending [CFS15, FI13], where lending is a flux of reserves and is proportional to the difference in reserves. A natural question is therefore how to estimate the interaction structure from the observation of the process. Unfortunately, the optimal solution based on the maximum likelihood estimator (MLE) is typically quite inaccurate in high-dimensional settings, because of the well-known curse of dimensionality, see for instance [BvdG11]. However, in real-world applications, the interaction structure is sparse: in the example mentioned above, banks have typically only a few lending partners [GG14, GSV15, BBvL15], as the lending arrangements are typically done on a personal level.

ABSTRACT A major challenge in computed tomography (CT) is to reduce X-ray dose to a low or even ultra-low level while maintaining the high quality of reconstructed images. We propose a new method for CT reconstruction that combines penalized weighted-least squares reconstruction (PWLS) with regularization based on a sparsifying transform (PWLS-ST) learned from a dataset of numerous CT images. We adopt an alternating algorithm to optimize the PWLS-ST cost function that alternates between a CT image update step and a sparse coding step. We adopt a relaxed linearized augmented Lagrangian method with ordered-subsets (relaxed OS-LALM) to accelerate the CT image update step by reducing the number of forward and backward projections. Numerical experiments on the XCAT phantom show that for low dose levels, the proposed PWLS-ST method dramatically improves the quality of reconstructed images compared to PWLS reconstruction with a nonadaptive edge-preserving regularizer (PWLS-EP).

We develop a model in which interactions between nodes of a dynamic network are counted by non homogeneous Poisson processes. In a block modelling perspective, nodes belong to hidden clusters (whose number is unknown) and the intensity functions of the counting processes only depend on the clusters of nodes. In order to make inference tractable we move to discrete time by partitioning the entire time horizon in which interactions are observed in fixed-length time sub-intervals. First, we derive an exact integrated classification likelihood criterion and maximize it relying on a greedy search approach. This allows to estimate the memberships to clusters and the number of clusters simultaneously. Then a maximum-likelihood estimator is developed to estimate non parametrically the integrated intensities. We discuss the over-fitting problems of the model and propose a regularized version solving these issues. Experiments on real and simulated data are carried out in order to assess the proposed methodology.

Several fundamental problems that arise in optimization and computer science can be cast as follows: Given vectors $v_1,\ldots,v_m \in \mathbb{R}^d$ and a constraint family ${\cal B}\subseteq 2^{[m]}$, find a set $S \in \cal{B}$ that maximizes the squared volume of the simplex spanned by the vectors in $S$. A motivating example is the data-summarization problem in machine learning where one is given a collection of vectors that represent data such as documents or images. The volume of a set of vectors is used as a measure of their diversity, and partition or matroid constraints over $[m]$ are imposed in order to ensure resource or fairness constraints. Recently, Nikolov and Singh presented a convex program and showed how it can be used to estimate the value of the most diverse set when ${\cal B}$ corresponds to a partition matroid. This result was recently extended to regular matroids in works of Straszak and Vishnoi, and Anari and Oveis Gharan. The question of whether these estimation algorithms can be converted into the more useful approximation algorithms -- that also output a set -- remained open. The main contribution of this paper is to give the first approximation algorithms for both partition and regular matroids. We present novel formulations for the subdeterminant maximization problem for these matroids; this reduces them to the problem of finding a point that maximizes the absolute value of a nonconvex function over a Cartesian product of probability simplices. The technical core of our results is a new anti-concentration inequality for dependent random variables that allows us to relate the optimal value of these nonconvex functions to their value at a random point. Unlike prior work on the constrained subdeterminant maximization problem, our proofs do not rely on real-stability or convexity and could be of independent interest both in algorithms and complexity.

Leasing is a popular channel to market new cars. Pricing a leasing contract is complicated because the leasing rate embodies an expectation of the residual value of the car after contract expiration. To aid lessors in their pricing decisions, the paper develops resale price forecasting models. A peculiarity of the leasing business is that forecast errors entail different costs. Identifying effective ways to address this characteristic is the main objective of the paper. More specifically, the paper contributes to the literature through i) consolidating and integrating previous work in forecasting with asymmetric cost of error functions, ii) systematically evaluating previous approaches and comparing them to a new approach, and iii) demonstrating that forecasting with asymmetric cost of error functions enhances the quality of decision support in car leasing. For example, under the assumption that the costs of overestimating resale prices is twice that of the opposite error, incorporating corresponding cost asymmetry into forecast model development reduces decision costs by about eight percent, compared to a standard forecasting model. Higher asymmetry produces even larger improvements.

With the proliferation of mobile devices and the internet of things, developing principled solutions for privacy in time series applications has become increasingly important. While differential privacy is the gold standard for database privacy, many time series applications require a different kind of guarantee, and a number of recent works have used some form of inferential privacy to address these situations. However, a major barrier to using inferential privacy in practice is its lack of graceful composition -- even if the same or related sensitive data is used in multiple releases that are safe individually, the combined release may have poor privacy properties. In this paper, we study composition properties of a form of inferential privacy called Pufferfish when applied to time-series data. We show that while general Pufferfish mechanisms may not compose gracefully, a specific Pufferfish mechanism, called the Markov Quilt Mechanism, which was recently introduced, has strong composition properties comparable to that of pure differential privacy when applied to time series data.

In the last years, the extension of deep neural network architectures towards recurrent processing of temporal data has opened the way to novel approaches to effectively learn hierarchical representations of time-series featured by multiple timescales dynamics [19, 18, 10, 9, 1]. Recently, within the umbrella of randomized neural network approaches [4], Reservoir Computing (RC) [21, 15] has proved to be a useful tool for analyzing the intrinsic properties of stacked architectures in recurrent neural networks (RNNs), allowing at the same time to exploit the extreme efficiency of RC training algorithms in the design of novel deep RNN models. Stemming from the Echo State Network (ESN) approach [12] the study of the dynamics of multi-layered recurrent reservoir architectures has been introduced with the deep-ESN model in [7, 5].

We study in this paper the consequences of using the Mean Absolute Percentage Error (MAPE) as a measure of quality for regression models. We prove the existence of an optimal MAPE model and we show the universal consistency of Empirical Risk Minimization based on the MAPE. We also show that finding the best model under the MAPE is equivalent to doing weighted Mean Absolute Error (MAE) regression, and we apply this weighting strategy to kernel regression. The behavior of the MAPE kernel regression is illustrated on simulated data.

The stochastic block model (SBM) is a flexible probabilistic tool that can be used to model interactions between clusters of nodes in a network. However, it does not account for interactions of time varying intensity between clusters. The extension of the SBM developed in this paper addresses this shortcoming through a temporal partition: assuming interactions between nodes are recorded on fixed-length time intervals, the inference procedure associated with the model we propose allows to cluster simultaneously the nodes of the network and the time intervals. The number of clusters of nodes and of time intervals, as well as the memberships to clusters, are obtained by maximizing an exact integrated complete-data likelihood, relying on a greedy search approach. Experiments on simulated and real data are carried out in order to assess the proposed methodology.