This is an abandoned scaffold, not the thesis

Last touched 21 April 2026 and never finished — its own status table marks Chapters 1, 2, 3, 5-Phase B and 6 as “Not started”, and its chapter scheme differs from what was actually defended. Kept for the record only.

The completed thesis is dated September 2026 and was defended 27 July 2026; the manuscript is not published here, but the defense deck is.

Master’s Thesis Draft

Item	Content
Name	Azwan Nazamuddin
Affiliation / Year	Graduate School of Innovation and Practice for Smart Society, Hiroshima University / M2
Supervisor	Prof. Makoto Chikaraishi
Thesis Title (tentative)	A Scalable Computational Framework for Activity-Based Dynamic Discrete Choice Models: Reachability, GPU Acceleration, and Baseline Estimation
Target Length	~80–100 pages (excluding appendices)
Last Updated	2026/04/21

---

How to use this draft

• This draft doubles as the “Research Overview Document” submitted for each lab meeting. Per-meeting discussion docs live in meetings/<semester>/.
• For unwritten parts, TODO: markers are used so it is clear at a glance which sections are still blank.
• The detailed planning outline — with tables, equations, and expected results — is kept in 3 - Permanent Notes/research-plan/MASTER_THESIS_OUTLINE.md. This draft is the prose version; the outline is the scaffold.
• Update this draft before each meeting. Old versions are preserved through Git history.

---

Chapter 1. Introduction (~10 pages)

1.1 Motivation

TODO:

• Have: MASTER_THESIS_OUTLINE.md §1.1 now structured as 4-move runway into the waist.
• Need: One concrete Higashihiroshima policy example to anchor Move 1 locally (e.g. peak-hour congestion on Route 2, or ageing population transit access in outer zones).
• Write: ~2 pages following the 4-move structure below:

Move 1 — Societal (½ page) Cities face welfare trade-offs in transport policy — congestion pricing, emissions, ageing populations, autonomous mobility. Planners need models that both predict behavioural response and measure welfare impact in monetary terms. Aggregate four-step models answer neither. [Cite: Vickrey 1969; Eliasson et al. 2009]

Move 2 — Why timing and chaining (½ page) Policies work through when people travel and which trips they chain. Static models fail for three reasons (de Palma & Fosgerau 2011): departure time is endogenous; scheduling costs equal travel-time costs (empirically 0.5–1.5× value of time, Small 1982); time-varying policies have no static analogue. Trip-chaining — work, child drop-off, shopping — compounds the problem. [Cite: de Palma & Fosgerau 2011; Vickrey 1969 (bottleneck model); Small 1982 (schedule delay cost magnitudes — NOT Vickrey)]

Move 3 — DDCM promise (½ page) Dynamic Discrete Choice Models (DDCMs) for activity-based travel demand (Västberg et al. 2020) answer both questions jointly: behavioural realism through dynamic utility maximisation, and a welfare measure through the log-sum value function (McFadden 1981; Small & Rosen 1981) — “a toll costs each household ¥X ± ¥Y per day”. The model continues to be actively developed (McCarthy, Karlström & Västberg 2025). [Cite: Västberg et al. 2020; McFadden 1981; Small & Rosen 1981; McCarthy et al. 2025]

Move 4 — Computational barrier (½ page) Exact computation requires backward induction through every reachable state. The state space grows exponentially: at Higashihiroshima scale, 146 million theoretical states, ~69 hours and 6.7 TB memory naive. At realistic city scale, Västberg et al. (2020) report ~1,000 CPU-days. Practitioners approximate — but approximation silently corrupts the welfare measure. This thesis demonstrates exact computation is achievable: reachability pruning reduces the state space by >99%, and GPU-accelerated backward induction completes in under 2 seconds at 1.5 million states. [Cite: Västberg et al. 2020]

1.2 The Two Barriers

• Barrier 1 — Computational Intractability. 8-dimensional state space ≈ 146M theoretical states; naive BI ≈ 69 h / 6.7 TB. Structural (curse of dimensionality), not hardware.
• Barrier 2 — Estimation Difficulty. Recovering θ requires repeatedly solving the DP. NFXP, MPEC, CCP, sampling each have limits at scale; no scalable method delivers analytical SEs without nested DP.

TODO:

• Have: Two-barrier framing already written as bullets; 146M / 6.7 TB / 69 h numbers from §3.1, §4; §2.5 comparison table (NFXP / MPEC / CCP / sampling / TD / PUM).
• Need: One-sentence preview for each estimation method so the reader understands the gap; reference for “no scalable method” claim.
• Write: Expand each bullet into ~1 page. Cross-reference §3.1 for state-space derivation. Close with the gap line as bridge into §1.3.

1.3 Research Objectives (Master Scope)

#	Objective
O1	Develop a scalable computational framework for exact inference in activity-based DDCMs through reachability-based state pruning, sparse graph representation, and GPU-accelerated backward induction.
O2	Demonstrate that city-scale DDCM is solvable exactly: implement NFXP estimation to convergence, recover coherent utility parameters, and characterise the identification structure of the estimated model.

O1 resolves Barrier 1. O2 resolves the core of Barrier 2 at master’s scope — NFXP converges and parameters are recovered. Remaining open items (sandwich SEs, welfare gradient SE(CV)) are Phase B, documented in §5.6 as future work motivating the PhD.

1.4 Scope and Contributions

• Geographic scope: Higashihiroshima, Japan (144 zones)
• Data: N=1,368 workers (current estimation subset), person-trip travel survey; full sample N≈3,000+ (pending expansion)
• Hardware: NVIDIA RTX 5090 32 GB (GPU estimation)

Master contributions:

1. DAG framing — DDCM as a Directed Acyclic Graph, enabling GPU-parallel level-by-level backward induction and shared-graph population handling.
2. Reachability pruning — forward BFS with Hägerstrand space-time prism constraints: 145M → 1.5M states (99% reduction), stored as CSR; exact, no approximation.
3. μ(t) utility profiles — time-varying marginal-utility specification (Supernak 1992; Joh et al. 2003) replacing hard time windows: activity timing and trip-making emerge from preference gradients, not model rules.
4. Analytical gradient + NFXP estimation — exact ∂ℓ/∂θ via second backward-induction pass; NFXP to convergence on city-scale data; identification analysis characterising the c_change likelihood ridge.

Note: RMDP abstraction was explored and dropped (see §4.5). The population-handling solution is the shared universal graph per activity-sequence group with individual constraints as masks (Contributions 1–2 jointly).

TODO:

• Have: Four contribution bullets resolved above.
• Need: None — utility spec decision resolved as μ(t).
• Write: 1–2 paragraphs linking the four contributions to Objectives (C1+C2+C3 → O1; C4 → O2) and framing them as a pipeline: DAG framing (§4.1) → reachability (§4.2) → sparse graph (§4.3) → GPU BI (§4.4) → μ(t) spec (§3.3), feeding Ch. 5 estimation.

1.5 Thesis Structure

TODO:

• Have: Chapter scaffold (this draft).
• Need: Stable chapter structure — wait until Ch. 4–6 first drafts are done.
• Write: One paragraph per chapter (~3 sentences). Template: “Chapter X develops [topic]; it [key method/result]; leading into Chapter X+1 which [next].” Finalise last.

---

Chapter 2. Background and Literature Review (~15 pages)

2.1 Activity-Based Travel Demand Models

TODO:

• Have: Reference list (Hägerstrand, TRANSIMS, MATSim) in MASTER_THESIS_OUTLINE.md §2.1.
• Need: Decide depth — full lit review or just enough context to motivate DDCMs.
• Write: ~2 pages. Close with one paragraph motivating the shift to DDCMs (welfare-consistent logsum is the payoff).

2.2 Dynamic Discrete Choice Models: Theory

TODO:

• Have: Rust (1987), logit-DDCM derivation portable from APTE paper §2 (4 - Projects/ddcm/).
• Need: Confirm notation consistency with Ch. 4–5 (s, a, θ, V̄).
• Write: ~3 pages. Include Bellman equation and logit-DDCM derivation inline; reference Appendix A.1 for the full derivation.

2.3 DDCMs in Transport

TODO:

• Have: @vastbergDynamicDiscreteChoice2020.md paper note; McCarthy et al. (2025) full paper at ddcm-core/ddcm_duration.md; Fosgerau, Frejinger & Karlström (2013) recursive-logit reference.
• Need: Short summary of recursive logit to position Västberg (2020) against it.
• Write: ~3 pages. Dedicate ~1.5 pages to Västberg (2020): state space, utility spec, Methods 1 & 2, computational limits that motivate Ch. 4. Add one paragraph on McCarthy et al. (2025) — confirms the KTH group is still actively developing SCAPER but the core computational barrier is unsolved. Closest section to the contribution.

2.4 Approaches to the Computational Curse

TODO:

• Have: Powell (2007) ADP reference; Oyama & Hato (2019) reachability.
• Need: Bansal et al. (2017) reachability-in-control paper lookup; one existing transport-GPU reference.
• Write: ~2 pages. End with Oyama & Hato (2019) as the bridge into §4.2 (reachability pruning).

2.5 Estimation Methods for DDCMs

TODO:

• Have: Comparison-table rows sketched in MASTER_THESIS_OUTLINE.md §2.5 (NFXP / CCP / MPEC / Sampling / TD / PUM).
• Need: Short paper summary per row (especially Adusumilli & Eckardt 2025 TD, Fosgerau et al. 2024 PUM).
• Write: ~3 pages. Build the comparison table first (method | key paper | approach | limitation), then prose per row. Close with the gap Ch. 5 confronts and the PhD resolves.

2.6 Research Gap Summary

TODO:

• Have: Nothing — depends on §2.1–§2.5.
• Need: Stable content in §2.1–§2.6.
• Write: ~0.5 page. Table: Gap | Addressed in | How. Write last.

---

Chapter 3. Model Specification (~12 pages)

3.1 The Higashihiroshima DDCM

TODO:

• Have: State-space table in MASTER_THESIS_OUTLINE.md §3.1; APTE paper draft has this content.
• Need: Zone map figure (if produced) or geographical prose description; explicit 146M product footnote.
• Write: ~3 pages. Port state-space table.

3.2 Action Space

TODO:

• Have: Feasibility rules listed in MASTER_THESIS_OUTLINE.md §3.2.
• Need: None.
• Write: ~2 pages. Numbered enumeration, one subsection per rule family (duration / time-window / mode-transition / ownership / terminal). Cross-reference §4.2 where these become BFS constraints.

3.3 Utility Function Specification

Decision resolved: μ(t) is the thesis utility specification. Classic Västberg schedule-delay penalties + hard time windows are described in §2.3 as the predecessor model. This thesis uses the μ(t) temporal profile framework.

K=10 parameter set (δ, α, β, β₁_shop, β₀_shop, β₁_leis, β₀_leis, c_change, μ_home, θ_travel). Full equations and profile types in ddcm_slides/slides.md §μ(t) and 260419 §3.3.

TODO:

• Have: Full μ(t) spec in 260419 §3.3; parameter table in ddcm_slides/slides.md.
• Need: None — spec is resolved.
• Write: ~3 pages. Four subsections: Home (flat floor), Work/School (piecewise δ/α/β), Shop/Leisure (P_open Gaussian-mixture), Travel (θ_travel scale). Display equations for each profile type. Close with the behavioural anchors (c_change and μ_home jointly set trip frequency). Grounded in Supernak (1992) and Joh et al. (2003) — do NOT frame as Västberg extension.

3.4 Data Description

TODO:

• Have: N=4700 loaded / 3331 valid / 217,885 steps / 35 timing groups; ownership rates (car 27.9%, motorcycle 2.3%, bicycle 17.7%); train_time=0 sentinel note from r14 report; raw data at data/OD_LOS_new.csv, data/zone_attractiveness_verified.csv.
• Need: Compute summary-stats table; document preprocessing steps.
• Write: ~3 pages. Three subsections (survey / OD LOS / zone attractiveness). Call out train_time=0 explicitly — it drives the train-share mismatch in §5.5 Finding 2.

3.5 Transition Function

TODO:

• Have: Stay / move / terminal cases in MASTER_THESIS_OUTLINE.md §3.5.
• Need: None.
• Write: ~1 page. Formalise T(s,a) per case. Keep short — interesting structure is in §3.2.

---

Chapter 4. Scalable Computational Framework (~18 pages)

Status: Content complete. Core source: ICMC 2025 + APTE 2026. Writing status: first draft to be assembled from existing reports.

4.1 The Computational Problem

TODO:

• Have: 146M / 69 h / 6.7 TB numbers (derived in §3.1).
• Need: None.
• Write: ~1 page. State the naive budget; end with the insight that only ~1% are physically reachable. Motivates §4.2–§4.5.

4.2 Reachability-Based State Pruning

TODO:

• Have: Algorithm 1 pseudocode in MASTER_THESIS_OUTLINE.md §4.2; figures forward_reachability_2d.png and forward_reachability_3d.png; 146M → 1.5M / 462M edges result.
• Need: None.
• Write: ~3 pages. Include Algorithm 1. Discuss Hägerstrand space-time prism connection. Report the 99% reduction.

4.3 Sparse Graph Representation (CSR Format)

TODO:

• Have: CSR array layout in MASTER_THESIS_OUTLINE.md §4.3; memory numbers.
• Need: Small worked example (3–4 nodes) for illustration.
• Write: ~2 pages. Quantify dense 2.25×10¹² entries vs CSR 6.5 GB. End with “fits in GPU VRAM” as handoff to §4.4.

4.4 GPU-Accelerated Backward Induction

TODO:

• Have: Algorithm 2 pseudocode in MASTER_THESIS_OUTLINE.md §4.4; ~1.5 s/BI-pass timing.
• Need: None.
• Write: ~3 pages. Include Algorithm 2. Explain gather → vectorised Q → scatter-reduce (logsumexp). Use “commodity GPU” in prose; move hardware brand details to Appendix C (writing-style rule).

4.5 Shared Universal Graph and Population Handling

The naive approach builds one graph per agent (N separate graphs). The insight: agents of the same activity-sequence type (e.g. “worker with car”) share the same feasibility rules and the same DAG structure. Individual constraints — home zone, diary time windows — are applied as masks at simulation time, not baked into the graph. Result: one graph per activity-sequence group covers the entire population. Four groups cover the Higashi-Hiroshima population.

Note on RMDP. A Relational MDP abstraction (Boutilier et al. 2001) with role-binding (HOME_ZONE as a runtime parameter) was explored as a more general formulation. It was dropped in favour of the simpler shared-graph-per-group approach: the RMDP formalism added theoretical overhead without changing the computational result.

TODO:

• Have: Shared-graph insight documented in 260419 §2 and §3.1; 4-group population structure in city-scale simulation.
• Need: Formal definition of activity-sequence group; enumeration of the 4 groups used for Higashi-Hiroshima.
• Write: ~1.5 pages. Frame the naive N-graphs problem, state the shared-graph insight, define the 4 groups, note masks. Keep RMDP as a brief footnote — do not build a section around it.

4.6 Optional Approximations

• Linear VFA — V(s) ≈ Φ(s)w; 9.1× speedup; error characterised.
• Spatially Interpolated BI — exact for subset, interpolate for others; 2.0× speedup.

TODO:

• Have: Linear VFA 9.1× and Interpolated BI 2.0× speedup numbers.
• Need: Specific error bounds (currently qualitative).
• Write: ~2 pages. Flag clearly as optional — default path (§4.2–§4.5) is exact. Qualitative language until error numbers are pinned down (avoid overclaiming).

4.7 Results

TODO:

• Have: Table 4.1 rows in MASTER_THESIS_OUTLINE.md §4.7; Table 4.2 rows.
• Need: None.
• Write: ~2 pages with Tables 4.1 and 4.2. Lead with qualitative framing (“tractable at city scale”), then numbers (writing-style rule).

4.8 Behavioural Validation (Simulation Check)

TODO:

• Have: 1,000-agent WORK simulation numbers (81% HOME at night; 43% at WORK 8–18h; mean 6.1 h work; 99.7% work starts 6–10 AM; mean 3.25 trips/agent).
• Need: None.
• Write: ~1.5 pages. Frame as simulation-level sanity check, not validation against observed survey (that is §5.4). Use “sanity check”, not “validation”.

---

Chapter 5. Estimation — Baseline and Identification Analysis (~18 pages)

Status: Phase A in progress (K=10, N=1,368 workers, BFGS + analytical gradient; best ℓ = −28,708.6, ‖∇ℓ‖∞ = 0.78 — partial convergence; c_change identification ridge under investigation). Phase B pending (sandwich SEs, welfare ∂V̄/∂θ, MaxEnt-IRL verification).

5.1 Estimation Problem Setup

TODO:

• Have: LL objective formula in MASTER_THESIS_OUTLINE.md §5.1.
• Need: None.
• Write: ~2 pages. State LL with display equations. End on V(s;θ) pain point (recomputed per θ candidate) as motivation for §5.2.

5.2 Sampling of Alternatives (Västberg 2020 Method 2)

TODO:

• Have: Method 2 algorithm in MASTER_THESIS_OUTLINE.md §5.2; McFadden (1981) correction reference.
• Need: McFadden correction derivation written out for Appendix A.2.
• Write: ~3 pages. Algorithm step-by-step. Close with caveats (frozen V̄ bias, sampling variance) that motivate NFXP (§5.3).

5.3 NFXP Implementation (K=10, μ(t))

Pipeline. Outer BFGS over K=10 parameters; inner backward induction on the pruned DAG for V̄(s;θ) and log-likelihood evaluation. Gradient via analytical differentiation of the Bellman recursion (Fosgerau et al. 2013): a second BI pass propagates ∂V̄/∂θ backward at the same cost order as the inner BI — exact, no finite differences.

Current estimation status (April 2026, best checkpoint iter 19):

Parameter	Description	θ̂
δ	On-schedule utility (per min)	0.0266
α	Earliness penalty rate	0.00102
β	Lateness penalty rate	0.00300
β₁_shop	Shop P_open sensitivity	0.281
β₀_shop	Shop base utility	−0.871
β₁_leis	Leisure P_open sensitivity	0.353
β₀_leis	Leisure base utility	−0.162
c_change	Activity-switching cost	−2.500 ⚠ bound
μ_home	Home floor utility	0.102
θ_travel	Travel disutility scale	2.00

Best ℓ = −28,708.6 · ‖∇ℓ‖∞ = 0.78 (threshold 0.001) · partial convergence — BFGS terminated at iter 35 with precision-loss message; c_change pinned at lower bound. δ and μ_home carry the expected positive signs.

Status: ⏳ Estimation pending full convergence. See §5.5 for identification diagnosis and §5.6 for pending items.

TODO:

• Have: K=10 parameter table from 260419 §7.2; pipeline description from 260419 §7.1 and ddcm_slides/slides.md.
• Need: Final converged parameter table (pending c_change resolution).
• Write: ~4 pages. Three subsections: (a) pipeline + BFGS + analytical gradient (why analytical: exact and same cost as inner BI); (b) current estimates with status; (c) convergence narrative. Replace this table with final converged estimates when available. Hardware details to Appendix C.

5.4 Behavioural Simulation Results

TODO:

• Have: Mode-share and activity-time simulation tables from simulation_metrics_nfxp.csv.
• Need: Observed columns alongside simulated columns for side-by-side comparison.
• Write: ~2 pages. Dedicated paragraph for the CHANGE=0 substantive finding — timing constraints absorb the role of explicit mode-change penalties. Do not bury as an aside.

5.5 Identification Analysis

Observed behaviour in current run. $c_{\text{change}}$ is pinned at its lower bound (−2.500) from early iterations; the gradient w.r.t. $c_{\text{change}}$ remained negative throughout. BFGS plateaued for 13 consecutive iterations at $\ell \approx -28,709$ before the “desired error not necessarily achieved due to precision loss” termination at iter 35. Activity parameters ($\delta$, $\alpha$, $\beta$, activity intercepts) barely moved from warm-start values. ${\theta }_{\text{travel}}$ ran off to 2.0, roughly double the MNL-aligned prior.

Suspected identification ridge. The likelihood has a shallow ridge along the $c_{\text{change}}$ direction. Because $c_{\text{change}}$ enters twice per trip (once per leg of each activity switch), it controls trip frequency regardless of activity utility. When $|c_{\text{change}}|$ is large, inertia reproduces any observed schedule, absorbing the data’s information about activity utilities into the switching cost — making those parameters weakly identified. This is an identification issue, not an optimiser issue: multi-start BFGS, tighter tolerances, or different step rules cannot fix a flat ridge.

Three-step diagnosis (in progress):

1. Score-sign check. Compute $\partial \ell /\partial c_{\text{change}}$ over a range of $c_{\text{change}}$ values; determine whether the gradient ever changes sign. If observed trip count exceeds predicted trip count at every reasonable $c_{\text{change}}$, the gradient is negative by construction and identification fails on structural grounds. Cost: design work only — no extra compute.
2. Profile-likelihood sweep over $c_{\text{change}}\in \{-2.5,-2.0,-1.5,-1.0,-0.5,-0.3,0\}$: seven warm-started BFGS runs (≈1–2 h each) at fixed $c_{\text{change}}$ values. Directly visualises the ridge. If $\ell$ is flat across this range, $c_{\text{change}}$ is not separately identified. If $\ell$ has a clear peak, that value is the concentrated MLE.
3. Paper-ready fallback: fix $c_{\text{change}}$ at the MNL switching-cost prior (−0.3) and estimate the remaining 9 parameters. Yields a fully identified submodel, presented honestly as “conditioning on the MNL switching-cost prior.” One overnight run.

Structural interpretation. If the ridge is confirmed, it is a model-scope limitation for the current data: the survey records individual trips but not the time-varying identity of co-travellers or chained-activity patterns that would separately pin the switching cost. Fixing $c_{\text{change}}$ does not bias the activity-utility parameters — it removes a degenerate basin from the search space and restores identifiability of the remaining nine parameters.

TODO:

• Have: Observed run behaviour and ridge diagnosis from 260419 §7.3–7.4; three-step plan.
• Need: Results of score-sign check (step 1) and profile-likelihood sweep (step 2) — expected within 2–3 weeks.
• Write: ~3 pages. Lead with the observed run behaviour (table of per-iteration LL if available), then explain the ridge mechanism, then present the diagnosis steps and results once available. Close with the structural interpretation — frame as model-scope limitation, not estimation failure.

5.6 Standard Errors and Welfare ⏳ Pending

• Sandwich SEs (Phase B0): computation attempted (nfxp_se_20260330_233406.csv); SE values empty — rerun/debug needed.
• Welfare measure V̄(s₀): available from r14 BI at θ̂; not yet reported.
• Welfare gradient ∂V̄/∂θ (Phase B1): not yet computed. One additional backward pass (~1.5 s). Required for SE(CV) via delta method.
• MaxEnt-IRL ≡ DDC-MLE verification (Phase B2): not yet done. Would confirm Bridge 1 at 1.5M-state scale.

TODO:

• Have: r14 BI V̄(s₀) available but not reported; SE attempt file nfxp_se_20260330_233406.csv with empty values.
• Need: (1) Sandwich SE rerun/debug; (2) welfare gradient ∂V̄/∂θ (Phase B1, one extra BI pass ~1.5 s); (3) MaxEnt-IRL ≡ DDC-MLE check (Phase B2).
• Write: Blocked on Phase B. Leave section as ⏳ Pending until results land — makes missing content obvious.

5.7 NFXP: What Was Eliminated vs What Remains

TODO:

• Have: Comparison-table rows in MASTER_THESIS_OUTLINE.md §5.7.
• Need: None.
• Write: ~1.5 pages. Lead with the table (scannable), then short prose per row. Bridge to Ch. 6 — make “remaining gaps” column explicitly the PhD agenda.

---

Chapter 6. Conclusion (~8 pages)

6.1 Summary of Contributions

• Contribution 1 — DDCM as a DAG (Theoretical Framework). Reformulated activity-based DDCM as computation on a time-ordered directed acyclic graph. Each time level is an independent layer; backward induction is a forward pass over the DAG. This framing makes GPU parallelism structurally natural and opens the door to the two PhD-direction bridges (GNN and RL).
• Contribution 2 — Reachability-Based State-Space Pruning (Computational). Forward BFS with Hägerstrand space-time prism constraints removes states no feasible itinerary can reach. Applied to a 144-zone Higashi-Hiroshima network: 145M → 1.5M states (99% reduction), 6.7 TB → 6.5 GB memory, ~69 h → ~105 s wall time. Stored as a CSR sparse graph; one universal DAG per activity-sequence group, with individual reachability as a mask.
• Contribution 3 — μ(t) Smooth Utility Profiles (Behavioural Specification). Replaced hard time-window rules with continuous marginal-utility profiles μₐ(t), grounded in Supernak (1992) and Joh et al. (2003). K=10 parameters; activity timing, duration, and trip chaining emerge endogenously from preference comparison. Simulated agents reproduce work peak timing, leisure spreading, and home dominance without any hard scheduling rules.
• Contribution 4 — Analytical Gradient + NFXP (Estimation). Implemented the analytical score ∂ℓ/∂θ via a second backward-induction pass (Fosgerau et al. 2013), replacing finite differences or derivative-free search. Outer BFGS drives convergence; each gradient evaluation costs 2× BI, not 20×. Current run (K=10, N=1,368 workers): partial convergence at ℓ = −28,708.6 with c_change identification issue under active diagnosis.

TODO:

• Have: Four contribution bullets, aligned with April 2026 presentation and 260419.
• Need: Final converged estimates (pending c_change resolution) to update C4 status line.
• Write: ~2 pages. One paragraph per contribution — what was achieved, how, why it matters. Do not re-state full numbers (those belong in Ch. 4/5). Note explicitly that RMDP was explored during framework design and dropped in favour of the shared-graph-per-group approach.

6.2 Limitations

• N=1,368 workers; behavioural simulation and model validation are qualitative at this stage. Welfare estimates pending SE computation.
• Transport LOS parameters (travel time, cost) are locally estimated from Higashi-Hiroshima MNL mode choice data (unpublished); treated as fixed in NFXP estimation — constrained estimation loses mode-preference variance.
• GPU implementation targets CUDA (NVIDIA RTX 5090); portability to AMD or Apple hardware requires kernel re-implementation.
• $c_{\text{change}}$ identification: switching cost is not separately identified from activity utilities under the current survey structure; diagnosis and paper-ready fallback are in progress (§5.5).

TODO:

• Have: Four limitation bullets, updated to K=10/current status.
• Need: None.
• Write: ~2 pages. Honest framing — each limitation as scope, not fatal flaw. The c_change identification issue is the most substantive; give it a dedicated paragraph, framing it as a data-structure limitation (no within-person mode-switching variation to pin the cost) rather than a model failure.

6.3 Future Work: Toward Scalable Welfare-Preserving Estimation (PhD Direction)

Remaining gaps motivating the PhD:

1. Welfare SEs not yet computed: sandwich SEs require ∂V̄/∂θ (Phase B1, one extra BI pass ≈1.5 s) and SE sandwich matrix (Phase B0 — debug run needed). Without these, CV confidence intervals are unavailable.
2. NFXP iteration cost ~22–31 min: each BFGS step requires two full backward-induction passes over 1.5M states. Acceptable at K=10 but will not scale to the full population (N≈3,000+) or to policy-counterfactual sensitivity analysis.
3. Bridge 1 (Ermon 2015: MaxEnt IRL ≡ logit DDC) verified theoretically; empirical verification at 1.5M-state scale with the DDCM likelihood still needed (Phase B2). Until verified, Structural-IRL remains grounded in theory alone.
4. Structural-IRL algorithm not yet built: Phase C is the PhD research direction — a welfare-preserving faster-than-NFXP algorithm derived from the two bridges (GNN backward pass via Bridge 2; MaxEnt RL objective via Bridge 1) with Z(θ) = exp(V̄(s₀;θ)) kept intact as a hard constraint.

TODO:

• Have: Four remaining-gaps list; Bridge 1 (Ermon 2015) and Bridge 2 (Dudzik & Veličković 2022) references.
• Need: Short framing of Structural-IRL and welfare-preservation as hard constraint.
• Write: ~3 pages. Introduce both bridges at conceptual level — keep heavy math out. Emphasise welfare consistency as a hard constraint, not an ergonomic preference (this is the contribution over the ML/AI-in-transport literature).

6.4 Concluding Remarks

TODO:

• Have: Nothing yet.
• Need: None.
• Write: ~1 page. Short closer: what was shown (city-scale DDCM is tractable without sacrificing welfare interpretation), what it enables (policy simulation, structural identification), what’s next (PhD). No new numbers, no new citations.

---

Appendices

Appendix A. Mathematical Derivations

• A.1 Logit Bellman equation derivation
• A.2 McFadden (1981) correction for sampled alternatives
• A.3 c_change identification diagnostic: score-sign check and profile-likelihood sweep

Appendix B. Data Description

• B.1 Person-trip survey: sampling, variables
• B.2 OD Level of Service: sources, preprocessing
• B.3 Zone attractiveness: variables and summary stats
• B.4 Mode-ownership distribution by person

Appendix C. Computational Details

• C.1 GPU implementation: PyTorch tensor ops used
• C.2 CSR construction algorithm
• C.3 Runtime profiling by pipeline stage
• C.4 Reproduction instructions (code and data)

Appendix D. Estimation Details

• D.1 All estimation runs: parameters, LL trajectories
• D.2 Full gradient diagnostic output at K=24
• D.3 Sensitivity analysis: varying R (number of alternatives)
• D.4 Bug history and fixes

---

References (Selected)

Foundational DDCM. Rust (1987); Hotz & Miller (1993); Västberg et al. (2020); Västberg (2024).

Computational Methods. Hägerstrand (1970); Oyama & Hato (2019); Boutilier, Reiter & Price (2001); Powell (2007).

Estimation Theory. McFadden (1981); Su & Judd (2012); Fosgerau, Paulsen & Rasmussen (2022); Adusumilli & Eckardt (2025).

Full reference list: 3 - Permanent Notes/research-plan/MASTER_THESIS_OUTLINE.md § References.

---

Appendix: Writing Status (Where I Am Now)

Chapter	Status	Notes
Ch. 1 Introduction	Not started	Scaffold only. Fill 1.1 Motivation first.
Ch. 2 Background & Literature Review	Not started	Scaffold only.
Ch. 3 Model Specification	Not started	Scaffold only. Ch. 3 content available in APTE paper draft.
Ch. 4 Scalable Computational Framework	Drafting — content complete	Ch. 4 content fully available (ICMC 2025 + APTE 2026). Port into prose.
Ch. 5 Estimation — Phase A	Drafting — content complete	NFXP r14 results in hand. § 5.1–5.5 portable from Phase A reports.
Ch. 5 Estimation — Phase B	Not started	Sandwich SEs + welfare ∂V̄/∂θ pending.
Ch. 6 Conclusion	Not started	Depends on § 5.6 results.

Phase-level status is tracked in 3 - Permanent Notes/research-plan/MASTER_THESIS_OUTLINE.md § Current Status.