Online inference with multi-modal likelihood functions
多峰似然函数下的在线推断
Let (Yt)t≥1 be a sequence of i.i.d. observations and {fθ,θ∈Rd} be a parametric model. We introduce a new online algorithm for computing a sequence (θˆt)t≥1, which is shown to converge almost surely to argmaxθ∈RdE[logfθ(Y1)] at rate O(log(t)(1+ε)/2t−1/2), with ε>0 a user specified parameter. This convergence result is obtained under standard conditions on the statistical model and, most notably, we allow the mapping θ↦E[logfθ(Y1)] to be multi-modal. However, the computational…