Speaker: Yaniv Fogel

M.Sc. student under the supervision of Prof. Meir Feder

Wednesday, January 3^th 2018 at 15:30

Room 011, Kitot Bldg., Faculty of Engineering

On the Problem of On-Line Learning with Log-Loss

Abstract

Broadly speaking, the task of inductive learning aims at utilizing past examples of data features and respective outcomes into a better prediction of the next outcome given its respective data sample.

In this talk we will consider the problem of on-line learning with respect to the logarithmic loss, where the learner provides a probability assignment for the next label given the past and current data features and the past labels.

Our first result is a class of new universal on-line probability assignment schemes based on the mixture approach.

Now, in classical learning, it is well known that there are model classes that can be learned in batch, but cannot be learned sequentially for adversarial data features and outcome sequences.

We show that for these model classes the proposed mixture schemes lead to a vanishing regret in the individual setting when the adversary is somewhat constrained.

In the stochastic setting we show that any on-line solution for the log-loss may be used to obtain a solution for a wide variety of loss functions.

School of Mechanical Engineering Seminar
Wednesday, March14, 2018 at 14:00
Wolfson Building of Mechanical Engineering, Room 206

TURBULENCE IN A LOCALIZED PUFF IN A PIPE

Alexander Yakhot

Department of Mechanical Engineering, Ben-Gurion University, Beersheva, Israel

We have performed direct numerical simulations of transient turbulence in a pipe flow for Re=2,250 which has been recognized as a threshold for an equilibrium puff. We investigated the structure of an individual puff by considering three-dimensional snapshots over a long time period. To assimilate the velocity data, we applied a conditional sampling based on the location of the maximum energy of the transverse (turbulent) motion. Specifically, at each time instance, we followed a turbulent puff by a three-dimensional moving-window centered at that location. We collected a snapshot-ensemble of the velocity fields acquired over 10,000 time instances (snapshots) inside the moving-window. The considered flow is intermittent and transitional. The velocity field inside the puff shows the dynamics of a developing turbulence. The localized puff is about 12-15 pipe diameters long and the flow regime upstream of its trailing edge and downstream of its leading edge is almost laminar. In the puff core, despite the low Reynolds number, the turbulence statistics becomes similar to a fully-developed turbulent pipe flow and the velocity profile becomes flat in the pipe core and logarithmic near the wall. It is shown that this “fully-developed turbulent gap” is very narrow being about two pipe diameters long.

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