Task $2.$ Our dataset consists of user's sessions in a e$-$commerce store. Let $I=I_1,I_2,$dots,$I_N$

be a set of $N$ available products. A session is a sequence $(s_1,s_2,$dots,$s_n)$ of products

browsed successively by the user, where $n$ is the length of the session and $s_1,s_2,$dots,$s_n$inI

are the browsed products. In the training dataset, for each session $(s_1,s_2,$dots,$s_n)$ we have

a target product $t$ being the next product browsed by the user directly after the session.

A session$-$based recommender system aims at predicting the target product on the basis

of the session. It returns a probability vector $(p_1,p_2,$dots,$p_N)$ where $p_i$ denotes the prob$-$

ability that the target vector is $I_i,$ for $i=1,2,$dots,$N.$ In practical applications, such a

probability vector enables to determine the $K|$ most probable products and display them

to the user.

Example:

Set of available products: $I=\{101,102,103,104,105\}.$

Sessions and target products:

$(101,102,103),104$

$(101,102,103),105$

$(103,102,101),102$

$(105,102,104),105$

$(103,102,103),101$

Recommendations:

$(0\mathrm{.}10,0\mathrm{.}20,0\mathrm{.}20,0\mathrm{.}20,0\mathrm{.}30)$ recommendation: $105$

$(0\mathrm{.}30,0\mathrm{.}10,0\mathrm{.}10,0\mathrm{.}40,0\mathrm{.}10)$ recommendation: $104$

$(0\mathrm{.}20,0\mathrm{.}20,0\mathrm{.}20,0\mathrm{.}20,0\mathrm{.}20)$ recommendation: $101($or any other product, be$-$

cause of equal probabilities$)$

$(0\mathrm{.}10,0\mathrm{.}40,0\mathrm{.}30,0\mathrm{.}10,0\mathrm{.}10)$ recommendation: $102$

$(0\mathrm{.}00,0\mathrm{.}50,0\mathrm{.}20,0\mathrm{.}00,0\mathrm{.}30)$ recommendation: $102$

How to evaluate such a recommender system? Please propose and discuss possible eval$-$

uation metrics. Can we use accuracy for evaluating such a recommender system?