Exponential weighted moving average (exponential weighted moving Average) __ Depth Learning

introduction of EMA 1, Evolutionary arithmetic average (weighted equal)-> weighted average (weighted unequal)-> moving average (about is only to take the most recent N-th data for calculation)-> bulk Normalization (BN) and various optimization algorithms of the basic EMA: is exponential decreasing weighted moving average, The weighted influence of each numerical value decreases exponentially with time, the more the data weighting influence is closer to the current time 2, the formula and understanding

vt=βvt−1+ (1−β) θt v T =βv t−1 + (1−β) θt v_t = \beta V_{t-1} + (1-\beta) \theta_{t}, in the formula Θtθt \theta_{t} for T-time The actual temperature, the coefficient ββ\beta indicates the speed of the weighted descent, the smaller the value the faster the weight decreases, the VT v T v_t is the value of the T-time EMA. When v0=0 v 0 = 0 v_0 = 0 o'clock, available: vt= (1−β) (θt+βθt−1+β2θt−2+...+βt−1θ1) v t = (1−β) (θt +βθt−1 +β2θt−2 + ...) +βt−1θ1) v_t = (1-\beta) (\theta_{t}+\beta\theta_{t-1}+\beta^{2}\theta_{t-2}+ ... +\beta^{t-1}\theta_{1}), as you can see from the formula: The weight coefficients of the daily temperature (Θθ\theta) are reduced exponentially, and the more data weighting influence is near the current time. In the optimization algorithm, we generally take β>=0.9β>= 0.9 \beta >= 0.9, and 1+β