The $k$ nearest neighbour learning rule (under the uniform distance tie breaking) is universally consistent in every metric space $X$ that is sigma-finite dimensional in the sense of Nagata. This was pointed out by C\'erou and Guyader (2006) as a consequence of the main result by those authors, combined with a theorem in real analysis sketched by D. Preiss (1971) (and elaborated in detail by Assouad and Quentin de Gromard (2006)). We show that it is possible to give a direct proof along the same lines as the original theorem of Charles J. Stone (1977) about the universal consistency of the $k$-NN classifier in the finite dimensional Euclidean space. The generalization is non-trivial because of the distance ties being more prevalent in the non-euclidean setting, and on the way we investigate the relevant geometric properties of the metrics and the limitations of the Stone argument, by constructing various examples.

Most existing crowd counting methods require object location-level annotation, i.e., placing a dot at the center of an object. While being simpler than the bounding-box or pixel-level annotation, obtaining this annotation is still labor-intensive and time-consuming especially for images with highly crowded scenes. On the other hand, weaker annotations that only know the total count of objects can be almost effortless in many practical scenarios. Thus, it is desirable to develop a learning method that can effectively train models from count-level annotations. To this end, this paper studies the problem of weakly-supervised crowd counting which learns a model from only a small amount of location-level annotations (fully-supervised) but a large amount of count-level annotations (weakly-supervised). To perform effective training in this scenario, we observe that the direct solution of regressing the integral of density map to the object count is not sufficient and it is beneficial to introduce stronger regularizations on the predicted density map of weakly-annotated images. We devise a simple-yet-effective training strategy, namely Multiple Auxiliary Tasks Training (MATT), to construct regularizes for restricting the freedom of the generated density maps. Through extensive experiments on existing datasets and a newly proposed dataset, we validate the effectiveness of the proposed weakly-supervised method and demonstrate its superior performance over existing solutions.

The geometry automated theorem proving area distinguishes itself by a large number of specific methods and implementations, different approaches (synthetic, algebraic, semi-synthetic) and different goals and applications (from research in the area of artificial intelligence to applications in education). Apart from the usual measures of efficiency (e.g. CPU time), the possibility of visual and/or readable proofs is also an expected output against which the geometry automated theorem provers (GATP) should be measured. The implementation of a competition between GATP would allow to create a test bench for GATP developers to improve the existing ones and to propose new ones. It would also allow to establish a ranking for GATP that could be used by "clients" (e.g. developers of educational e-learning systems) to choose the best implementation for a given intended use.

In Part 3 of our series on how utilities are using artificial intelligence, we look at how AI amplifies analytics for grid operations. Duke Energy saved some $130 million in avoided costs by using predictive data analytics to identify problems before they caused equipment failures. A utility in Brazil estimates savings in the range of $420,000 USD each month through better, analytics-based theft detection. Because, as an article published by Forbes notes, "Machine learning is a continuation of the concepts around predictive analytics, with one key difference: The AI system is able to make assumptions, test and learn autonomously." With these enhancements, data science will become more powerful than ever, and utilities stand to gain.

Complex systems often require descriptions covering a wide range of scales and organization levels, where a hierarchical decomposition of their description into components and sub-components is often convenient. To better understand the hierarchical decomposition of complex systems, in this work we prove a few essential results that contribute to the development of an information-theory for hierarchical-partitions.

Weak supervision is a popular method for building machine learning models without relying on ground truth annotations. Instead, it generates probabilistic training labels by estimating the accuracies of multiple noisy labeling sources (e.g., heuristics, crowd workers). Existing approaches use latent variable estimation to model the noisy sources, but these methods can be computationally expensive, scaling superlinearly in the data. In this work, we show that, for a class of latent variable models highly applicable to weak supervision, we can find a closed-form solution to model parameters, obviating the need for iterative solutions like stochastic gradient descent (SGD). We use this insight to build FlyingSquid, a weak supervision framework that runs orders of magnitude faster than previous weak supervision approaches and requires fewer assumptions. In particular, we prove bounds on generalization error without assuming that the latent variable model can exactly parameterize the underlying data distribution. Empirically, we validate FlyingSquid on benchmark weak supervision datasets and find that it achieves the same or higher quality compared to previous approaches without the need to tune an SGD procedure, recovers model parameters 170 times faster on average, and enables new video analysis and online learning applications.

We study the estimation of risk-sensitive policies in reinforcement learning problems defined by a Markov Decision Process (MDPs) whose state and action spaces are countably finite. Prior efforts are predominately afflicted by computational challenges associated with the fact that risk-sensitive MDPs are time-inconsistent. To ameliorate this issue, we propose a new definition of risk, which we call caution, as a penalty function added to the dual objective of the linear programming (LP) formulation of reinforcement learning. The caution measures the distributional risk of a policy, which is a function of the policy's long-term state occupancy distribution. To solve this problem in an online model-free manner, we propose a stochastic variant of primal-dual method that uses Kullback-Lieber (KL) divergence as its proximal term. We establish that the number of iterations/samples required to attain approximately optimal solutions of this scheme matches tight dependencies on the cardinality of the state and action spaces, but differs in its dependence on the infinity norm of the gradient of the risk measure. Experiments demonstrate the merits of this approach for improving the reliability of reward accumulation without additional computational burdens.

A planning domain, as any model, is never complete and inevitably makes assumptions on the environment's dynamic. By allowing the specification of just one domain model, the knowledge engineer is only able to make one set of assumptions, and to specify a single objective-goal. Borrowing from work in Software Engineering, we propose a multi-tier framework for planning that allows the specification of different sets of assumptions, and of different corresponding objectives. The framework aims to support the synthesis of adaptive behavior so as to mitigate the intrinsic risk in any planning modeling task. After defining the multi-tier planning task and its solution concept, we show how to solve problem instances by a succinct compilation to a form of non-deterministic planning. In doing so, our technique justifies the applicability of planning with both fair and unfair actions, and the need for more efforts in developing planning systems supporting dual fairness assumptions.

Data volumes in mobile networks are increasing at an unprecedented rate. In our latest mobility report, we forecast that mobile data traffic will grow fourfold by 2025, reaching up to 160 exabytes (EB) per month. This is amazing of course and offers all kinds of opportunities for communications service providers, but there is also a potential downside to this rapid surge in data traffic: its impact on the energy consumption and carbon footprint of mobile networks. That's not the only downside for communications service providers, as it also raises a significant cost concern. As we found in our AI report, the demand to reduce operational costs already ranks among the top priorities for today's operators.

Training deep neural networks is an important problem which is still far from solved. At the core of the problem is our still relatively poor understanding of what happens under the hood of a deep neural network. Practically, this translates to a wide variety of deep network architectures and activation functions used in them. They all, however, suffer from the same problem when it comes to interpretability. It is next to impossible to understand how and why even a single layer network performs a simple classification task, and this probelm only increases with the size and the depth of the network. Activation functions stem from Cybenko's seminal 1989 paper [1], which proved that sigmoidal functions are universal approximators. This gave rise to a number of sigmoidal activation functions, including the sigmoid, tanh, arctan, binary step, Elliott sign [2], SoftSign [3] [4], SQNL [5], soft clipping [6] and many others. Sigmoidal activations were useful in the early days of neural networks, but the most serious problem that they suffered from was vanishing gradients.