Parallel predictive entropy search

⚠️ Curated Limitations & Negative Results

• Compactness alone does not guarantee finite attained maxima for arbitrary sample functions. A posterior maximizer target, tie-selection convention and finite information must be well defined. The displayed noisy-incumbent factor assumes a nonempty history and positive sigma; the record does not specify a general zero-noise, singular-covariance or empty-history implementation.
• Official NIPS 2015 main PDF has 9 pages; its linked ZIP contains a separate 2 page supplement. arXiv 1511.07130v1 was submitted November 23, 2015 and has 12 pages including the appendix. The checked method and appendix displays retain the same substantive caveats; publication, submission and PDF build dates are kept distinct. No author implementation was inspected or executed.
• Main Eq 4 on p.4 omits normalization, while supplement Eq 1 uses proportionality. Main Eq 5 and supplement Eq 3 give a malformed Gaussian mean update with a vector-plus-matrix sum and inverse. The covariance part is the supported precision-addition form. The record does not certify a literal implementation of the printed mean formula.
• Supplement p.1 Eq 5 has a site sum stopping at Q despite Q+1 sites and inconsistent parameter notation. On p.2, Eq 7 uses projected inverse covariance instead of the projected covariance in the cavity-variance calculation; Eq 11 uses squared cavity mean where the derivative identity requires squared cavity variance; beta for the soft site contains an extra Phi; Eqs10–11 omit the soft-probit noise-dependent moment factors; Eq 13 inverts a natural-mean difference that should be multiplied by the site variance. These are inspected source algebra caveats, not a claimed author erratum or complete repaired PPES implementation.
• The posterior-mean maximizer is not generally the posterior mode of the maximizer location. A finite three-point Gaussian example with means (1,0,0) and variances (0.01,100,100) gives the first point a win probability below one third, despite its uniquely highest mean; symmetry gives each other point a larger optimizer probability. The supporting audit uses an analytic upper bound and a differentiable-kernel realization, not Monte Carlo estimation.
• Converged EP site parameters can depend on the prior. For one standard zero-threshold Gaussian truncation with prior variance v, the projected variance is c v, c = 1 - 2/pi, and site precision is (1/c - 1)/v. The derivative through refitting is c, whereas freezing the site gives c^2. This bounded counterexample refutes general site constancy; it does not implement the complete PPES acquisition or audit all hypotheses of its cited EP references.
• Finite random features, approximate maximizer search, relaxed conditioning, Gaussian EP projection, rejected failed EP samples, Monte Carlo hyperparameters and local batch optimization all affect the operational approximation. The Figure 1 reference calculation itself uses discretization, rejection sampling and a kernel-density entropy estimate. The p.7 experimental prose says 200 random initializations while the Figure 3 caption on p.8 says 100; no aggregate empirical count or performance conclusion is adopted. No exact noisy information, unbiased accepted-sample, global-optimization, universal accuracy, runtime or superiority claim is made.
• The original bounded checks in research/discovery/ppes-boundaries.py use rational matrices and finite information channels, plus explicitly floating Gaussian CDF, moment and entropy calculations. They are supporting algebra and counterexamples, not full EP inference, external-code execution, a GP benchmark or independent scientific approval. Scalar PES, scalar optimum-value MES/OPES and constrained multi-objective PPESMOC remain distinct operational identities; the Q = 1 ideal-information overlap does not identify their approximations.