The spiked model
The synchronization problem and its semidefinite programming relaxations
Connection with n-vector spin glasses
Optimal local algorithms
Sum of squares hierarchy
The statistic/computation gap
Connection with sparse principal component analysis
Statistical applications
Applications to feature learning and topic models
Convex and iterative algorithms
Phase transition under the spiked model
Back-propagation algorithm
Approximation theory
Convolutional networks
Connections with statistical physics