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We investigate robust linear regression where data may be contaminated by an oblivious adversary, i.e., an adversary than may know the data distribution but is otherwise oblivious to the realizations of the data samples. This model has been previously analyzed under strong assumptions. Concretely, (i) all previous works assume that the covariance matrix of the features is positive definite; and (ii) most of them assume that the features are centered (i.e. zero mean). Additionally, all previousarXiv:2202.02080v1 fatcat:2zotdtdxkje7na3lwgivpyw67y
more »... orks make additional restrictive assumption, e.g., assuming that the features are Gaussian or that the corruptions are symmetrically distributed. In this work we go beyond these assumptions and investigate robust regression under a more general set of assumptions: (i) we allow the covariance matrix to be either positive definite or positive semi definite, (ii) we do not necessarily assume that the features are centered, (iii) we make no further assumption beyond boundedness (sub-Gaussianity) of features and measurement noise. Under these assumption we analyze a natural SGD variant for this problem and show that it enjoys a fast convergence rate when the covariance matrix is positive definite. In the positive semi definite case we show that there are two regimes: if the features are centered we can obtain a standard convergence rate; otherwise the adversary can cause any learner to fail arbitrarily.
In numerical simulations we use κ = 10 and τ = 0.01. 2 We have studied (Horn, Levy, & Ruppin, 1996) a similar mechanism for the extreme case of synaptic deletion in the context of a model for Alzheimer's ...doi:10.1162/089976698300017863 pmid:9501502 fatcat:xtdy5pggsvbytd5igxf22666e4
Motivated by the findings of modular structure in the association cortex, we study a multi-modular model of associative memory that can successfully store memory patterns with different levels of activity. We show that the segregation of synaptic conductances into intra-modular linear and inter-modular nonlinear ones considerably enhances the network's memory retrieval performance. Compared with the conventional, single-module associative memory network, the multi-modular network has two maindblp:conf/nips/LevyHR97 fatcat:ry3w2vmhcbecfc5sd6zcezh6xe
more »... vantages: It is less susceptible to damage to columnar input, and its response is consistent with the cognitive data pertaining to category specific impairment.
ACKNOWLEDGEMENTS We greatly appreciate fruitful discussions with Paz London, Aharon Blank, Efrat Lifshitz, Vladimir Dyakonov, Sergey Tarasenko, Victor Soltamov, Nadav Katz, Michael Stern and Nir Bar-Gil ...arXiv:1904.04783v1 fatcat:m4zd5d243vdwrh2oixr72stbxi
In this paper, we design mother wavelets for the 1D continuous wavelet transform with some optimality properties. An optimal mother wavelet here is one that has an ambiguity function with minimal spread in the continuous coefficient space (also called phase space). Since the ambiguity function is the reproducing kernel of the coefficient space, optimal windows lead to phase space representations which are "optimally sharp." Namely, the wavelet coefficients have minimal correlations with eacharXiv:2104.01654v1 fatcat:u5m2qnqm4zf6fb2b4spl7stn3m
more »... er. Such a construction also promotes sparsity in phase space. The spread of the ambiguity function is modeled as the sum of variances along the axes in phase space. In order to optimize the mother wavelet directly as a 1D signal, we pull-back the variances, defined on the 2D phase space, to the so called window-signal space. This is done using the recently developed wavelet-Plancharel theory. The approach allows formulating the optimization problem of the 2D ambiguity function as a minimization problem of the 1D mother wavelet. The resulting 1D formulation is more efficient and does not involve complicated constraints on the 2D ambiguity function. We optimize the mother wavelet using gradient descent, which yields a locally optimal mother wavelet.
This model, and its reduction to account for multiple viruses and virus strains in one population, is presented by Levy et al.  . ...arXiv:1902.04073v1 fatcat:m6zmg5yzcjgjlbjc7uhnytbkwm
Recent imaging studies suggest that object knowledge is stored in the brain as a distributed network of many cortical areas. Motivated by these observations, we study a multi-modular associative memory network, whose functional goal is to store patterns with di erent coding levels, i.e., patterns that vary in the number of modules in which they are encoded. We show that in order to accomplish this task, synaptic inputs should be segregated into intra-modular projections and inter-modulardoi:10.1162/089976699300016205 pmid:10490944 fatcat:icbsfqg7cve4nbzewk2wl3fwiq
more »... ions, with the latter undergoing additional nonlinear dendritic processing. This segregation makes sense anatomically if the inter-modular projections represent distal synaptic connections on apical dendrites. It is then straightforward to show that memories encoded in more modules are more resilient to focal a erent damage. Further hierarchical segregation of inter-modular connections on the dendritic tree improves this resilience, allowing memory retrieval from input to just one of the modules in which it is encoded. 0
Combined bNIRS and EEG headgear was custom built for simultaneous acquisition of NIRS and EEG data and consisted of a NIRS headband and an EEG cap. ... Light sources used in traditional NIRS systems typically emit light at 2 or 3 wavelengths in the NIR range, which allow users to resolve changes in HbO 2 and HHb concentrations only. ...doi:10.1038/s41598-021-83420-9 pmid:33597576 pmcid:PMC7889942 fatcat:7aftl3ay6fdkfhuvim4jt4a66i
Levy and Rizansky  investigate the utility of health and wealth by interviewing cancer and diabetes patients about their health-wealth tradeoffs. ...doi:10.1371/journal.pone.0113894 pmid:25422889 pmcid:PMC4244177 fatcat:e5v7mie2jnftfhympafexqoauy
The search-and-matching model of the labor market fails to match two important business cycle facts: (i) a high volatility of unemployment relative to labor productivity, and (ii) a mild correlation between these two variables. We address these shortcomings by focusing on technological learning-by-doing: the notion that it takes workers' time using a technology before reaching their full productive potential with it. We consider a novel source of business cycles, namely, fluctuations in thedoi:10.1111/iere.12093 fatcat:y2ptky64wnbz3kh66bm3424b5m
more »... d of technological learning, and show that a search-and-matching model featuring such shocks can account for both facts. Moreover, our model provides a new interpretation of recently discussed "news shocks.
In this paper we introduce a new localization framework for wavelet transforms, such as the 1D wavelet transform and the Shearlet transform. Our goal is to design nonadaptive window functions that promote sparsity in some sense. For that, we introduce a framework for analyzing localization aspects of window functions. Our localization theory diverges from the conventional theory in two ways. First, we distinguish between the group generators, and the operators that measure localization (calledarXiv:1707.04863v3 fatcat:xqju6uujnrg7xjcosw42xdqlgi
more »... bservables). Second, we define the uncertainty of a signal transform based on a window as a whole, instead of defining the uncertainty of an individual window. We show that the uncertainty of a window function, in the signal space, is closely related to the localization of the reproducing kernel of the wavelet transform, in phase space. As a result, we show that using uncertainty minimizing window functions, results in representations which are optimally sparse in some sense.
In the framework of an associative memory model, we study the interplay between synaptic deletion and compensation, and memory deterioration, a clinical hallmark of Alzheimer's disease. Our study is motivated by experimental evidence that there are regulatory mechanisms that take part in the homeostasis of neuronal activity and act on the neuronal level. We show that following synaptic deletion, synaptic compensation can be carried out efficiently by a local, dynamic mechanism, where eachdoi:10.1162/neco.19220.127.116.117 pmid:8768393 fatcat:ya42qlb5izhblbdpfcxta7uyoq
more »... maintains the profile of its incoming postsynaptic current. Our results open up the possibility that the primary factor in the pathogenesis of cognitive deficiencies in Alzheimer's disease (AD) is the failure of local neuronal regulatory mechanisms. Allowing for neuronal death, we observe two pathological routes in AD, leading to different correlations between the levels of structural damage and functional decline.
See also Figure S7 . same transcript (Shomron and Levy, 2009) . ... ., 2009; Levy et al., 2010) . Like the initial step of miRNA processing, RNA splicing occurs cotranscriptionally in the nucleus (Kornblihtt, 2007; Luco et al., 2011) . ...doi:10.1016/j.molcel.2013.05.007 pmid:23747012 fatcat:nmkqjainjvdmza6y3mvjql3ss4
Type I chaperonins play an essential role in the folding of newly translated and stress-denatured proteins in eubacteria, mitochondria and chloroplasts. Since their discovery, the bacterial chaperonins have provided an excellent model system for investigating the mechanism by which chaperonins mediate protein folding. Due to the high conservation of the primary sequence among Type I chaperonins, it is generally accepted that organellar chaperonins function similar to the bacterial ones.doi:10.1016/s0014-5793(02)03178-2 pmid:12354603 fatcat:pskv2oddnfdtroaddvdyxhsehy
more »... recent studies indicate that the chloroplast and mitochondrial chaperonins possess unique structural and functional properties that distinguish them from their bacterial homologs. This review focuses on the unique properties of organellar chaperonins. ß 2002 Published by Elsevier Science B.V. on behalf of the Federation of European Biochemical Societies.
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