The recursive teaching dimension (RTD) of a concept class C {0,1}n, introduced by Zilles et al. [ZLHZ11], is a complexity parameter measured by the worst-case number of labeled examples needed to learn any target concept of C in the recursive teaching model. In this paper, we study the quantitative relation between RTD and the well-known learning complexity measure VC dimension (VCD), and improve the best known upper and (worst-case) lower bounds on the recursive teaching dimension with respect to the VC dimension. Given a concept class C {0,1}n with VCD(C) = d, we first show that RTD(C) is at most d 2d+1. This is the first upper bound for RTD(C)that depends only on VCD(C), independent of the size of the concept class |C| and its domain size n. Before our work, the best known upper bound for RTD(C) is O(d2d loglog|C|), obtained by Moran et al. [MSWY15].

Generative state estimators based on probabilistic filters and smoothers are one of the most popular classes of state estimators for robots and autonomous vehicles.

Air strikes have targeted the headquarters of the Iran-aligned Popular Mobilisation Forces (PMF) in Iraq's capital, Baghdad, as the country becomes a two-way battlefield between armed factions and the United States during its war with Iran . The US carried out strikes against the Shia paramilitary umbrella group, also known locally as Hashed al-Shaabi, late on Sunday after attacks on a US diplomatic and logistics centre at Baghdad International Airport. The attack was carried out after Iraqi security officials said four explosions were heard near Camp Victory, a US logistics centre at the capital's main airport. Al Jazeera's Assed Baig, reporting from Baghdad, said some drones "breached air defences and caused damage, more symbolic damage than anything else". "At the same time, Iraqi security forces have set up checkpoints around Baghdad to try and stop these drone strikes because some of these factions are launching drones from the vicinity of Baghdad," he said.

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How does our motor system solve the problem of anticipatory control in spite of a wide spectrum of response dynamics from different musculo-skeletal systems, transport delays as well as response latencies throughout the central nervous system? To a great extent, our highly-skilled motor responses are a result of a reactive feedback system, originating in the brain-stem and spinal cord, combined with a feed-forward anticipatory system, that is adaptively fine-tuned by sensory experience and originates in the cerebellum. Based on that interaction we design the counterfactual predictive control (CFPC) architecture, an anticipatory adaptive motor control scheme in which a feed-forward module, based on the cerebellum, steers an error feedback controller with counterfactual error signals. Those are signals that trigger reactions as actual errors would, but that do not code for any current or forthcoming errors. In order to determine the optimal learning strategy, we derive a novel learning rule for the feed-forward module that involves an eligibility trace and operates at the synaptic level. In particular, our eligibility trace provides a mechanism beyond co-incidence detection in that it convolves a history of prior synaptic inputs with error signals. In the context of cerebellar physiology, this solution implies that Purkinje cell synapses should generate eligibility traces using a forward model of the system being controlled. From an engineering perspective, CFPC provides a general-purpose anticipatory control architecture equipped with a learning rule that exploits the full dynamics of the closed-loop system.

Aisasetofweightedlinear combinations of the entries ofX, this problem is often referred to as thematrix sensingproblem.

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Deep neural networks (DNNs) have demonstrated state-of-the-art results on many pattern recognition tasks, especially vision classification problems. Understanding the inner workings of such computational brains is both fascinating basic science that is interesting in its own right--similar to why we study the human brain--and will enable researchers to further improve DNNs. One path to understanding how a neural network functions internally is to study what each of its neurons has learned to detect. One such method is called activation maximization (AM), which synthesizes an input (e.g. an image) that highly activates a neuron. Here we dramatically improve the qualitative state of the art of activation maximization by harnessing a powerful, learned prior: a deep generator network (DGN). The algorithm (1) generates qualitatively state-of-the-art synthetic images that look almost real, (2) reveals the features learned by each neuron in an interpretable way, (3) generalizes well to new datasets and somewhat well to different network architectures without requiring the prior to be relearned, and (4) can be considered as a high-quality generative method (in this case, by generating novel, creative, interesting, recognizable images).

We propose a stochastic optimization method for the minimization of the sum of three convex functions, one of which has Lipschitz continuous gradient as well as restricted strong convexity. Our approach is most suitable in the setting where it is computationally advantageous to process smooth term in the decomposition with its stochastic gradient estimate and the other two functions separately with their proximal operators, such as doubly regularized empirical risk minimization problems. We prove the convergence characterization of the proposed algorithm in expectation under the standard assumptions for the stochastic gradient estimate of the smooth term. Our method operates in the primal space and can be considered as a stochastic extension of the three-operator splitting method. Numerical evidence supports the effectiveness of our method in real-world problems.

Practical applications of machine learning often involve successive training iterations with changes to features and training examples. Ideally, changes in the output of any new model should only be improvements (wins) over the previous iteration, but in practice the predictions may change neutrally for many examples, resulting in extra net-zero wins and losses, referred to as unnecessary churn. These changes in the predictions are problematic for usability for some applications, and make it harder and more expensive to measure if a change is statistically significant positive. In this paper, we formulate the problem and present a stabilization operator to regularize a classifier towards a previous classifier. We use a Markov chain Monte Carlo stabilization operator to produce a model with more consistent predictions without adversely affecting accuracy. We investigate the properties of the proposal with theoretical analysis. Experiments on benchmark datasets for different classification algorithms demonstrate the method and the resulting reduction in churn.