t	time step
$D_i^s$	set of activities for which i-th sensor node should send $d_{i,t}$ to the main node
D	set of all recognized activities (activities are denoted by natural numbers, $D_i^s\subset D$)
$d_{i,t}$	activity recognized by sensor node i at time step t
$d_t$	activity recognized by the main node at time step t based on the voting procedure
$w\left(d_{i,t}\right)$	weight of the recognized activity ($w\left(d_{i,t}\right)\in [0,1]$)
$s_{i,t}$	binary variable, which describes the necessity of sending $d_{i,t}$ to the main node
$M_i$	machine learning model used by i-th sensor node
$X_i\left(t\right)$	time series of sensor readings collected by node i at time step t
a	accuracy of activity recognition
$ϵ$	tuning parameter, which helps to neglect the influence of outliers