Question 1

Weighted undirected gene regulatory network (Figure 1) with nodes Ra, Y6, Z1, G1, G2, X1, Y1 and edge weights, plus question text about W[Z1, {blue, yellow, green}] Assume we are using a logistic regression model to estimate the probability of a protein pair $(u, v)$ to truly interact based on two features $X_{uv}^1$ and $X_{uv}^2$. Let $\beta_0$ be the intercept and $\beta_1$ and $\beta_2$ be the weights of the features $X_{uv}^1$ and $X_{uv}^2$ respectively. In the trained model, $\hat{\beta}_1 = 1.1$ and $\hat{\beta}_2 = 0.4$. For a protein pair with $X_{uv}^1 = 0.6$ and $X_{uv}^2 = 3$, this trained model predicted the probability of interaction to be 0.7427. What will this model predict for the probability of interaction of another protein pair with $X_{uv}^1 = 1$ and $X_{uv}^2 = -1$? Figure from the original question paper