We consider the random-design least-squares regression problem within the reproducing kernel Hubert space (RKHS) framework. Given a stream of independent and identically distributed input/output ...data, we aim to learn a regression function within an RKHS ℋ, even if the optimal predictor (i.e., the conditional expectation) is not in ℋ. In a stochastic approximation framework where the estimator is updated after each observation, we show that the averaged unregularized least-mean-square algorithm (a form of stochastic gradient descent), given a sufficient large step-size, attains optimal rates of convergence for a variety of regimes for the smoothnesses of the optimal prediction function and the functions in ℋ. Our results apply as well in the usual finite-dimensional setting of parametric least-squares regression, showing adaptivity of our estimator to the spectral decay of the covariance matrix of the covariates.
In this paper, we give a complete form of bijective (not necessarily linear) maps Formula omitted. where H,K are Hilbert spaces with Formula omitted. that satisfy Formula omitted. where Formula ...omitted. is the λ-Aluthge transform of T and the operation Formula omitted. is the Formula omitted. -Jordan-triple product. We show that there exists a unitary or anti-unitary operator Formula omitted. and a constant Formula omitted. , with Formula omitted. such that Formula omitted.
in this paper, we give a concept of szl -widering mapping which is independent of nonspreading mappings, k - strictly pseudo nonspring mappings and nonexpansive mappings. Also we introduce a new ...proximal point schemes of resolvent and szl -widering mappings. On the other hand, we discuss that the weak and strong convergence for these proximal point schemes in real Hilbert space under different conditions to asymptotic common fixed point of szl -widering mappings.
Abstract We prove sharp universal upper bounds on the number of linearly independent steady and asymptotic states of discrete- and continuous-time Markovian evolutions of open quantum systems. We ...show that the bounds depend only on the dimension of the system and not on the details of the dynamics. A comparison with similar bounds deriving from a recent spectral conjecture for Markovian evolutions is also provided.
The aim of this article is to propose a new definition of fuzzy fractional derivative, so-called fuzzy conformable. To this end, we discussed fuzzy conformable fractional integral softly. Meanwhile, ...uniqueness, existence, and other properties of solutions of certain fuzzy conformable fractional differential equations under strongly generalized differentiability are also utilized. Furthermore, all needed requirements for characterizing solutions by equivalent systems of crisp conformable fractional differential equations are debated. In this orientation, modern trend and new computational algorithm in terms of analytic and approximate conformable solutions are proposed. Finally, the reproducing kernel Hilbert space method in the conformable emotion is constructed side by side with numerical results, tabulated data, and graphical representations.
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