Partha Mitra

Bassam Bamieh, Mihailo R. Jovanović, Partha Mitra et al.

We consider distributed consensus and vehicular formation control problems. Specifically we address the question of whether local feedback is sufficient to maintain coherence in large-scale networks subject to stochastic disturbances. We define macroscopic performance measures which are global quantities that capture the notion of coherence; a notion of global order that quantifies how closely the formation resembles a solid object. We consider how these measures scale asymptotically with network size in the topologies of regular lattices in 1, 2 and higher dimensions, with vehicular platoons corresponding to the 1 dimensional case. A common phenomenon appears where a higher spatial dimension implies a more favorable scaling of coherence measures, with a dimensions of 3 being necessary to achieve coherence in consensus and vehicular formations under certain conditions. In particular, we show that it is impossible to have large coherent one dimensional vehicular platoons with only local feedback. We analyze these effects in terms of the underlying energetic modes of motion, showing that they take the form of large temporal and spatial scales resulting in an accordion-like motion of formations. A conclusion can be drawn that in low spatial dimensions, local feedback is unable to regulate large-scale disturbances, but it can in higher spatial dimensions. This phenomenon is distinct from, and unrelated to string instability issues which are commonly encountered in control problems for automated highways.

Mikhail Belkin, Daniel Hsu, Partha Mitra

Many modern machine learning models are trained to achieve zero or near-zero training error in order to obtain near-optimal (but non-zero) test error. This phenomenon of strong generalization performance for "overfitted" / interpolated classifiers appears to be ubiquitous in high-dimensional data, having been observed in deep networks, kernel machines, boosting and random forests. Their performance is consistently robust even when the data contain large amounts of label noise. Very little theory is available to explain these observations. The vast majority of theoretical analyses of generalization allows for interpolation only when there is little or no label noise. This paper takes a step toward a theoretical foundation for interpolated classifiers by analyzing local interpolating schemes, including geometric simplicial interpolation algorithm and singularly weighted $k$-nearest neighbor schemes. Consistency or near-consistency is proved for these schemes in classification and regression problems. Moreover, the nearest neighbor schemes exhibit optimal rates under some standard statistical assumptions. Finally, this paper suggests a way to explain the phenomenon of adversarial examples, which are seemingly ubiquitous in modern machine learning, and also discusses some connections to kernel machines and random forests in the interpolated regime.

Yuncong Chen, Lauren McElvain, Alex Tolpygo et al.

While modern imaging technologies such as fMRI have opened exciting new possibilities for studying the brain in vivo, histological sections remain the best way to study the anatomy of the brain at the level of single neurons. The histological atlas changed little since 1909 and localizing brain regions is a still a labor intensive process performed only by experienced neuro-anatomists. Existing digital atlases such as the Allen Brain atlas are limited to low resolution images which cannot identify the detailed structure of the neurons. We have developed a digital atlas methodology that combines information about the 3D organization of the brain and the detailed texture of neurons in different structures. Using the methodology we developed an atlas for the mouse brainstem and mid-brain, two regions for which there are currently no good atlases. Our atlas is "active" in that it can be used to automatically align a histological stack to the atlas, thus reducing the work of the neuroanatomist.