Corrections

[tlienart]

General (need follow up)

• [x] in chap 7, alg 13, check notations for indexing the nodes
• [x] in chap 7, define the target for EP and provide a figure to illustrate the node update in alg13
• [x] Provide a better justification of the experimental settings in ~Chap 3, 4, 6~ and 7. ~In particular, in 4.2.4 mention caveats limitations of experimental analysis regarding HMC (leapfrog steps, stepsize). Provide a description of data preproc~
  • [x] chap 3
  • [x] chap 4 + caveats + data preproc
  • [x] chap 6
  • [x] chap 7
• [x] clarify statement regarding consistency throughout the doc and ~in particular in chap3~. ~Give references and definition for consistency of SMC smoothers~
  • [x] chap 3 + reference and definition for SMC (smoothers)
  • [x] EPBP consistency thing
  • [x] rest of doc - chasing
    • [x] p ~12 "importance sampling is consistent"
    • [x] p ~21 "approximated consistently via integral"
    • [x] p ~29 "consistent" for BIS
    • [x] p ~34 (just before 3.2.3)
    • [x] p ~42 "estimators are not consistent"
    • [x] p ~73 "consistent messages"
    • [x] p ~95 "does not lead to consistent estimators of LBP"
    • [x] p ~97 "consistent estimators of LBP messages"
    • [x] p ~98 "consistent with LBP iterations"
    • [x] p ~105 (EPBP)
    • [x] p ~111 "consistent estimators of LBP messages"
• [x] In 2.3 provide a picture to explain the bouncy PS and provide a more detailed description of the hyperparams of the algorithm
• [x] clarify contribution with respect to published work with co-authors in chap 6
• [x] fix notation for damping parameter kappa/d in fig 6.2

RT (can follow up)

fixes from RT to follow up on

• [x] p37 graphs for things. probably goes with description of setup
• [x] p40 same
• [x] comment on reasoning for data/methods for chap 1 (see p41)
• [x] p45 (naive gibbs + footnote)
• [x] p48, 49, 50, 51 comments
• [x] p64 notation
• [x] p71 comment
• [x] p75 check comment (normalisation?)
• [x] p78 algo check
• [x] p82, say a little about where comes from
• [x] p83, revisit + add inner reference
• [x] p85 MSE etc
• [x] p86 more about Bregman
• [x] p87, help reader + maybe discuss what these experiments entail (basically say that wanted to show on a simple model can do better than a more complex framework and it's dubious .. )
• [x] p92, explain what goes wrong if conditions don't hold
• [x] p97, helpful...
• [x] p98 justify + small fixes
• [x] p99 come back
• [x] p100 come back
• [x] p101-109 come back (EPBP experiments)
• [x] (in conclusion) discuss metrics (see p111, 112 rt), basically you can use log lik (so?)

Smaller (no need follow up)

PDMP

• [x] NR - mention also works with truncated distributions / truncated domains?

Consistency fix

• SMC estimators converge in distribution (CLT) --> not consistency (should not use consistency for smoothing etc)
• IS estimators converge a.s. under usual condition --> consistent (should use consistency for EPBP)
• For PF p(x_t | y_{1:t}) converges a.s. under mild condition (http://jimbeck.caltech.edu/summerlectures/references/Particle%20smoother.pdf)
• Crisan & Doucet 2000, convergence in MSE, can be extended to smoothing estimators (cf. previous citation)
• Conclusion: should distinguish. For the PF, PS, use Crisan & Doucet and extension Godsill, Doucet and West. For general SMC, keep weaker result (convergence in distribution, saying there are a number of technical results and cite). In general remove "consistent" as you're either talking about a convergence of the measure (in which case it's AS using PF/PS result) or about the estimator itself (for EPBP) where it's IS and therefore actually consistent.
• Lit:
  • Survey of convergence results: http://www.cs.ubc.ca/~arnaud/crisan_doucet_survey.pdf
  • Variance estimation of PF: https://arxiv.org/pdf/1509.00394.pdf
  • PF tutorial: http://www.cs.ubc.ca/~arnaud/doucet_johansen_tutorialPF.pdf (section 3.6)
  • CLT for PF: http://www.cs.ubc.ca/~arnaud/doucet_johansen_tutorialPF.pdf
  • SMC samplers: https://www.stats.ox.ac.uk/~doucet/delmoral_doucet_jasra_sequentialmontecarlosamplersJRSSB.pdf

final

• [x] introduce notation for set (singleton, see p4)

• [x] add citation for RTS smoother on p6 (e.g.: http://adsabs.harvard.edu/abs/1965AIAAJ...3.1445R)

• [x] remove \simiid from algos unless true, prefer "sample ... from ..."

• [x] in HMM example specify data randomised too

• [x] when mentioning HMM or MRF --> HMMs or MRFs

  • [x] HMMs
  • [x] MRFs

• [x] chase blank spaces

• [x] best seen (not viewed) in colour (without s)

[tlienart]

Modifications in chap 2

~In 2.3 provide a picture to explain the bouncy PS and provide a more detailed description of the hyperparams of the algorithm~

• added figure 2.1 fig:bounce-bps and figure 2.2 fig:bps-trajec to clarify the specular reflection as well as the process along a trajectory (bouncing times)
• clarified that the key elements when deploying BPS = lambdaref and sampling of IPP

~Define consistency clearly (p12 importance sampling, p21 integral)~

• Added precise definition of consistency of IS estimator citing Robert and Casella
• Clarified the convergence of the BPS estimator citing theorem 1 of Bouchard 15.
• Added a small section on the Convergence of particle filters and smoothers citing the CLT result of Chopin 2004 for SMC methods, the review of convergence results for the PF by Crisan and Doucet and the convergence result for a PS by Godsill et al.

[tlienart]

Modifications in chap 3

~clarify consistency statement + add reference to consistency of SMC (smoother)~

• replaced "consistency" by convergence in distribution (CLT) which is guaranteed for SMC methods by chopin04 + see section 2.2.4 for relevant citations.

~better justification of experimental setting~ (RT) ~p37 graphs for things. probably goes with description of setup, p40 same, comment on reasoning for data/methods for chap 1 (see p41)~

• clarified that the data is randomised for every experiment
• clarified that the aim of the experiments is to present the simplest possible models in which a clear difference in performance among algorithms is shown + justification for error metric.
• for 1st experiment clarified explicitly that goal is to show FH underperforms and sub-sampled methods don't.
• clarified the legends of the violin plot to explain in more details what is represented.
• added that further work could consider computational performances more in depth along with more adequate error metric (log lik on held-out)

[tlienart]

Modifications in chap 4

~better justification of the experimental settings + caveats of HMC setup + discussion of preprocessing~ (RT) ~p45 (naive gibbs + footnote)~~ p48, 49, 50, 51 comments~

• mentioned that the block gibbs sampler could be used + reference
• clarified the setup with the SVD for the baseline explaining that the ratings are centered around zero and that the recovered low-rank reconstruction is much less sparse than original matrix.
• clarified the preprocessing of the ratings to be centered and scale onto [-1, 1]
• clarified that 2 leapfrog steps is usually not enough but was chosen for computational reasoning
• clarified how the test-RMSE is computed exactly adding an explicit equation 4.10
• clarified that the stepsize could be adapted and that generally HMC results could be improved but we ran it like that in order to "be fair" wrt local BPS which is still in infancy

[tlienart]

Modifications in chap 5

(RT) ~p64 notation~, ~p71 comment~

• clarified that the problem with cycles and BP may not converge + if does, may be multiple FP

Modifications in chap 6

(G) experimental setting; ~consistency p +- 73 "consistent messages"~ ~(G) clarify contribution vs published paper~ ~(G) fix notation d/k in figures~ (RT) ~p75 check comment (normalisation?)~ ~p78 algo check~ ~p82, say a little about where comes from~ ~p83, revisit + add inner reference~ ~p85 MSE etc~ ~p86 more about Bregman~ ~p87, help reader + maybe discuss what these experiments entail (basically say that wanted to show on a simple model can do better than a more complex framework and it's dubious .. )~

• clarified explicitly the novelty brought in the chapter at the beginning of the chapter as well as the aim of the chapter (simple experiment etc)
• clarified where \mathcal G equation came from
• added more details to the legend of figure 6.2 to indicate what was represented and clarify the symbols used for damping.
• added precise reference to what algorithm corresponds to what equation

[tlienart]

Modifications in chap 7

(G) Consistency fix p ~95 "does not lead to consistent estimators of LBP"

• clarified that LBP leads to biased estimators of the LBP messages

p ~97 "consistent estimators of LBP messages", p ~105 (EPBP) p ~111 "consistent estimators of LBP messages"

• clarified that "clean LBP" leads to IS estimators with almost sure convergence guarantees whereas PBP with approximate sampling does not

(G) ~Better justification of experimental setting~

(G) in chap 7, alg 13, check notations for indexing the nodes

• fixed

(G) in chap 7, ~define the target for EP~ and ~provide a figure to illustrate the node update in alg13~

• added the target explicitly (before 7.13)
• an extra page is added detailing the two phases of the EPBP node update along with two illustrations.

(RT) ~general fixes~ ~p92, explain what goes wrong if conditions don't hold~

• clarified that iteration would explode + message representation is ill defined

~p97, helpful...~, ~p98 justify + small fixes~ ~p99 come back~ ~p100 come back~ p101-109 come back (EPBP experiments)

• clarified that the models are chosen to exhibit specific properties in a controllable environment (mildly multimodal, non-gaussian setting) + that even though simple setting, it's already clear that EPBP > PBP
• made the error calculation explicit (MAE) eq 7.17
• added explicit justification for the example in the image denoising (non integrable edge potentials)

Modifications in ccl

(RT) (in conclusion) ~discuss metrics (see p111, 112 rt), basically you can use log lik (so?)~

• added explitly that proper metrics for Bayesian ML should be log likelihood on held out set or such

[tlienart]

fa8acd0 first finished pass, need to check cosmetics, write short report and done.

[tlienart]

35f2c78