Ordered sequential mining [8], PrefixSpan [9], SPADE [10] and episode mining [1] define temporal pattern semantics. Apriori [11], FP-growth [12], adaptive stream model maintenance [13] and count-min summaries [14] motivate distinct counting and adaptation choices. The present campaign uses unordered itemsets in transaction windows, so its results do not evaluate ordered episodes or sequences.

The proposed forgetting design defines exponential decay, while the evaluated implementation uses fixed and adaptive sliding windows. These memory choices have distinct support semantics and neither guarantees candidate coverage or cross-client quality.

Concept drift and adaptation have been studied across changing streams [2], [3], [15]. DDM monitors online classification error for evidence of change [16], ADWIN tests differences between subwindows and adjusts its window [17], and change-detection methods for streams treat the sampling assumptions explicitly [18]. Page’s CUSUM is a sequential-change method [19]. These approaches supply possible local alarm mechanisms; their nominal error control does not automatically transfer to the repeatedly inspected, temporally dependent itemset summaries evaluated here.

A detected change can motivate a window reset, candidate refresh or model update. Existing drift detectors and stream models [13] provide local mechanisms; this study asks how their reported outputs support distributed windowed itemsets. It compares event responses with scheduled refresh at the stated settings, without asserting absence of every prior federated adaptation method.

Federated learning studies coordination [4], communication [5], heterogeneity [6], [7], [20], proximal local work [21], and adaptive server optimization [22]. Resource-based client selection [23] has a different purpose from data-driven change alarms. Label-noise studies [24] illustrate corrupted supervision; their results do not establish the validity of a consensus-agreement weight for event-count quality.

Table 1 positions the reviewed method families. AdaFed-TPM proposes event-triggered refresh and consensus weighting for time-indexed patterns. The measured realization uses unordered itemsets, window replacement, and carry-forward supports; ordered episodes, geometric forgetting, and a formal stability floor remain outside the evaluated evidence.

RQ1 asks whether the reported event-response mechanism reduces modeled uplink payload relative to scheduled fixed-window refresh while tracking the same planted itemsets. Adaptation delay and re-discovery must be read alongside recall and bytes. The study includes no centralized drift-aware oracle and no complete network-traffic accounting; its results answer this question only for the stated stream generator, baselines, and checkpoint budget.

RQ2 asks whether agreement-based client weights add measurable value when corruption and arrival volume differ. The two ablations compare variants at the tested settings; they neither independently identify true client quality nor separate corruption from volume. A minority client may disagree because its population is different, so the weights also require a bias analysis before use as a trust score.

RQ3 concerns whether an explicitly specified forgetting or expiry rule improves adaptation without excessive pattern churn. The executed campaign uses two fixed window lengths rather than the decayed-support design in Eq. (1), and it does not report Jaccard-stability trajectories. Thus the decay-rate and stability questions remain prospective.

H1 asks whether event-responsive refresh can reduce uplink payload at acceptable adaptation delay relative to scheduled synchronization. Since heartbeats occur every checkpoint, sublinear total communication in stream length is not implied.

H2 asks whether consensus-based weighting improves discovery under quality degradation without suppressing genuinely different populations. This is an empirical hypothesis, not a variance-optimality or correctness guarantee.

H3 is a prospective hypothesis: an experimentally varied expiry or decay schedule may change the stability-delay trade-off. This campaign supplies no decay-rate sweep or evidence for the direction or existence of an optimum.

Client i observes a timestamped stream over a shared item alphabet, and the coordinator maintains pattern set P_t at checkpoints. Data quality may change, and an agreement score in [0,1] serves as a heuristic rather than a ground-truth corruption probability. The design assumes reliable communication. The campaign uses six clients, a common global stream, common planted drift times, and a fixed volume-corruption gradient; it does not implement a privacy mechanism.

R_t Set of clients refreshing at epoch t Subset of clients J_t Pattern-set stability index at t [0, 1] V(t) Uplink payload in interval; excludes downlinks bytes b_pat, b_hb, b_hdr Payload sizes: Pattern, heartbeat, header bytes

For a transaction window at epoch τ, let N_τ be its transaction count and n_τ(X) the number of transactions containing itemset X, with 0 ≤ n_τ(X) ≤ N_τ. Eq. (1) weights occurrence counts and transaction exposure by the same recency factor, so its rate has transaction-level support units and is defined only for positive weighted exposure. For clients with different window sizes, aggregate the weighted occurrence and exposure masses before forming a pooled rate; averaging client rates alone changes the population target. An idle epoch with N_τ = 0 adds neither mass; in the absence of fresh exposure the normalized rate stays constant, even as both old masses decay. Retraction therefore needs an explicit zero-occurrence exposure window or a separate expiry rule. The reported campaign implements fixed and adaptive transaction windows, not this proposed exponential-decay design.

−λ(t−τ)

∑τ≤t e nτ(X)

s (X, t) = . (1)

λ −λ(t−τ)

∑τ≤t e Nτ The design objective in Eq. (2) uses a hypothetical pooled drift-aware reference P*_t and a stability floor. Such a reference would need explicit construction and authorization in a future evaluation; it was not computed in this campaign. The implemented windowed heuristic does not establish optimality or satisfaction of the complete objective.

⋆ (2)

max ∑ F1 (Pw, Pw), subject to ∑ V (t) ≤ Btotal, Jt ≥ Jmin.

w=1 t

At checkpoints and local alarms, clients can refresh window summaries and the coordinator can update a carried-forward ledger. The general design below uses decayed support; Section 5 reports a windowed alternative with a long scheduled window and a short event window.

In the proposed decayed-support variant, a client would update candidate counts and exposure mass through Eq. (1). In the evaluated variant, itemsets are mined from fixed or adaptive transaction windows.

The general design permits the statistic of Eq. (3), subject to calibration. The reported implementation instead monitors vector summaries and pattern supports with its specified CUSUM alarms.

The proposed refresh rule sends digests after eligible alarms and heartbeats in inactive checkpoint rounds; Section 5 describes the implemented top-candidate event messages. The actual message trace is needed to audit charged bytes and carried-forward values.

The coordinator combines available or carried-forward summaries under the declared weighting rule. The reported campaign does not identify these weights with independent corruption probabilities, pooled population rates, or a privacy guarantee.

A bounded working set limits storage and update cost; it can miss patterns absent from local and global candidate routes. Maintaining k arbitrary itemsets requires at least their relevant membership tests per event unless an index or shared structure supplies a cheaper update. O(1) is meaningful only with a fixed k and fixed pattern length; it is not independent of candidate-set size. Count-min approximates queried counts [14] but does not itself enumerate unknown patterns.

The standardized two-window mean difference in Eq. (3) is one proposed change statistic, meaningful when its denominator is positive and its summary is scalar. If both variances vanish, define g=0 for equal means and g=+infinity for unequal means. A normal quantile alone does not control repeated sequential false alarms. The campaign uses a different vector-summary and per-pattern CUSUM with configured allowance and threshold [19], rather than a calibration of Eq. (3).

|μ ̂i(t) − μ ̂i(t − W)| gi(t) = .

√(vi(t) + vi(t − W))/W

Agreement with a leave-one-out consensus is a heuristic proxy for consistency, not an independent quality measurement. Under Non-IID streams a correct minority client may legitimately disagree. Eq. (4) sharpens score differences with a quadratic weight, but no noise model shows this is inverse-variance or optimal. A population support estimate uses pooled occurrence and exposure masses; precision-mixture weighting intentionally changes that target.

Qi(t)

wi(t) = . (4)

∑ ̂ ( )2 j Qj t If all agreement scores are zero, use a declared fallback such as uniform weights among available clients; the implementation convention must be confirmed. Updating a score only when a digest arrives leaves a silent client's score stale; an EWMA does not automatically age it. The campaign compares top-15 probe supports with other received or carried-forward supports. These are already communicated values, but unchanged bytes do not constitute privacy protection, and carrying stale peer values can affect the agreement signal.

Decay of raw occurrence mass alone does not imply decay of normalized support when its denominator decays equally. An idle client requires an explicit zero-occurrence exposure window or support-expiry rule before stale patterns are retracted. Eq. (5) reports Jaccard stability, with J_t=1 when both sets are empty. Deferring removals does not guarantee J_t>=J_min when new additions enlarge the union; a hard constraint would need to validate the entire proposed set. The campaign does not log J_t or enforce a reported stability floor.

|Pt ∩ Pt−1|

Jt = . (5)

|Pt ∪ Pt−1| Eq. (6) accounts for uplink payload in interval t, including scheduled refresh clients R_t, idle heartbeats, and all intra-interval event responses A_t. Each event response e has a responding client set C_e and itemset payload count k_ie. The expression excludes downlink broadcasts, transport and cryptographic headers, retries, and encoding overhead unless those are charged into the payload constants. Regular heartbeats alone require communication linear in the number of checkpoints, and arbitrary alarms may occur throughout a stream. Event-sensitive digest savings therefore do not establish a sublinear total-communication theorem. The event term sums each responding client’s reported candidate payload and header over all alarms in the interval.

Vup(t) ≤ ∑ (kitbpat + bhdr) + (m − |Rt|)bhb + Vevent(t) .

i∈Rt Algorithm 1. AdaFed-TPM epoch at checkpoint t.

Input: streams E_i, decay lambda, window W, thresholds h_i, payload sizes b_pat, b_hb, b_hdr, stability floor J_min 1: for every client i = 1..m in parallel do 2: update decayed local supports s_i,lambda(X, t) via Eq. (1) 3: maintain local pattern set P_i^loc(t) by decayed-support ranking 4: compute drift statistic g_i(t) via Eq. (3) on windowed summaries 5: if g_i(t) > h_i then compile digest (top patterns + evidence); 6: send digest to server and join refresh set R_t 7: else send heartbeat only 8: end for 9: server: update reliability Qhat_i(t) from digest agreement 10: compute weights w_i(t) via Eq. (4); merge decayed supports 11: prune global set by decayed-support floor; compute J_t via Eq. (5) 12: if a hard stability floor is required, validate the entire proposed set; otherwise report J_t 13: broadcast delta (P_t vs P_{t-1}) to all clients Output: P_t, weights w_i(t), stability J_t, communication V(t)

For a fixed working set, decayed updates use bounded work per event; candidate expansion and counting depend on working-set size and pattern length. Count-min update cost depends on sketch depth, not generically on log k [14]. A refresh includes itemset identifiers, support values, and evidence, while silent clients send heartbeats. Server ranking and reliability comparisons add work beyond summation. These are design costs; actual campaign tables report a simulated uplink byte model.

Several failure modes follow from the proposed mechanisms. Section 5 reports adaptation delay and dead-pattern re-discovery on the simulated planted changes. The other mechanisms below require targeted tests or a replay of individual alarms and digests before their frequency and causal role can be estimated.

A change invisible to the monitored summaries need not trigger a local alarm. The evaluated short and long windows can then continue to carry stale supports until refreshed; decay would require the separate implementation specified above.

Repeated false alarms can increase the event-response term in Eq. (6). The source reports aggregate alarm counts, but without per-client timestamps and messages it does not isolate false-alarm payload.

Agreement-based weighting can favour clients already near the carried-forward consensus and suppress legitimate minority patterns. The source does not provide an independent probe of this feedback or show that the moving average prevents it.

A new item absent from current candidates requires a documented discovery or expansion path before its pattern can enter the global set. No bound on this delay follows from the reported experiment.

The reported experiment mines unordered itemsets from a synthetic transaction stream derived from the UCI Adult census corpus [25]. All 45,222 complete records are discretised into 23 binary items covering age band, education band, weekly-hours band, work class, sex, high income, capital gains and losses, US nativity, marital status, and occupation group. The background stream of 10,000 transactions resamples Adult baskets non-uniformly over three education strata whose mixture weights vary sinusoidally with stream position (amplitude 0.15, period 10,000), so a slow background drift rides on top of the planted events. Six disjoint three-itemset pattern groups are planted on this background: each group joins three mutually exclusive items of one categorical block (for example the three age bands), so its natural Adult support is below 0.05%, and injected occurrences give each group a base support of 0.06 before drift. Two abrupt drift events change the planted supports: at t = 3,333 pattern P1 is damped by a factor of 0.3, P2 is amplified by 3.0, and P3 dies; at t = 6,666 the same triple of changes is applied to P4, P5, and P6, with P6 newly appearing. The stream is routed to six clients with arrival weights proportional to 0.5, 0.8, 1.1, 1.4, 1.7, and 2.0 (realised shares 6.7% to 26.7%), and data quality is inversely paired with volume: the highest-volume client corrupts 20% of its items and the lowest-volume client 2%, with each present item dropped with probability q and each absent item inserted with probability q/23.

Four federations are compared on identical seeded streams. The global fixed-window federation mines a shared sliding window of 1,000 transactions and merges client digests by pooled volume. The federated periodic-retrain baseline re-mines every checkpoint on the 500-transaction retrain interval and merges identically. The local-adaptive baseline gives each client a CUSUM-shrunk window (250 transactions after an alarm, regrowth by 250 per checkpoint up to 1,000) and merges unweighted. AdaFed-TPM runs the same per-client batch CUSUM as the local-adaptive baseline (local batches of 25 transactions, L1 deviation of the 23-dimensional item-frequency vector against a reference estimated from the first 200 local transactions and re-estimated after each alarm, allowance k = 1.75, threshold h = 2.0, cooldown 100 local transactions, plus a per-pattern support CUSUM over the client's 25 monitored itemsets) and implements the reported combination of: quality-weighted aggregation with weights equal to the square of a reliability EWMA (blending 0.7/0.3) of the agreement between each digest's top-15 probe itemsets and the other clients' reported supports; a two-timescale window (a scheduled long window of 1,000 transactions for stability and an event window of 250 for candidates that moved near a drift); and drift-triggered immediate synchronisation of the top-50 candidates by relative support move, with 20-byte heartbeats in place of full digests whenever a client's pattern set overlaps its last sent digest by Jaccard at least 0.75 and no alarm fired, the server carrying silent clients' last supports forward. Two ablations remove the quality weighting (uniform weights) and the drift-triggered synchronisation. All mining uses a shared compact bitmask Apriori [11] over itemsets of at most three items, local minimum count 3, and a global minimum support rate of 0.008; the coordinator checkpoint interval is 500 transactions, giving 20 checkpoints per stream.

The source reports tracking recall, drift-response delay in checkpoint units, dead-pattern re-discovery, and a declared uplink accounting of 32 bytes per itemset and 20 per heartbeat, including event-sync responses. Mean and standard deviation summarize ten seeded streams. The source reports Python 3.12, NumPy [26], SciPy [27], statsmodels [28], Matplotlib [29], and 55.5 s runtime. Analysis timing, exact payload records, scripts, raw trajectories and artifacts are required to confirm these reports; preregistration is not documented.

Table 3 reports mean recall 0.988 for AdaFed-TPM versus 0.983 for fixed-window, 0.929 for local adaptive windows, and 0.869 for periodic retraining. The reported paired Wilcoxon contrast with retraining is W=0,p=0.0020 over ten seeds. The fixed-window contrast has Holm p=0.112, which supplies no evidence of a difference but does not establish equivalence. Uplink payload is 1066974 versus 1525188 bytes for fixed-window, a 30.0% reduction, and about 1.6% higher than retraining's 1050272 bytes. These are simulation payload comparisons, not total network-traffic measurements.

Fig. 1 reports per-checkpoint trajectories. Periodic retraining mean recall falls to 0.825 at the second checkpoint after the first drift and reaches a minimum 0.720. The damped planted support 0.018 is 2.25 times the 0.008 pruning threshold; short-window sampling variability is a possible explanation, not a demonstrated causal decomposition. Local adaptation reaches minimum 0.775, while AdaFed-TPM and fixed-window remain at least 0.950 and 0.900 in the reported means.

Dashed vertical lines mark the two drift events (t = 3,333 and t = 6,666); checkpoints occur every 500 transactions (Fig. 1).

After the first drift, fixed-window has mean adaptation delay 2.90 checkpoint windows, retraining 3.80, local adaptive windows 4.00 with SD 1.90, and AdaFed-TPM 4.00 with SD 1.10. Retraction of P3 is part of this metric, so carried-forward supports can prolong delay. After the second drift, both AdaFed-TPM and fixed-window have delay 1.00 with SD 0.00, while retraining and local adaptive windows have 1.20 with SD 0.60. The reported table therefore shows a tie, not a uniquely fastest proposed method.

Delay counts checkpoints until every drift-affected pattern's reported status matches its post-drift status; drift 1 therefore penalises the retraction of the dead pattern P3, while drift 2 requires only the pickup of live patterns.

The reported dead-pattern re-discovery rate is 0.115 for AdaFed-TPM versus 0.033 for retraining, about 3.5 times as large; the paired source test favours retraining (W=0,p=0.0020). A carried-forward support can retain a dead pattern until refreshed. Fixed-window has the shortest first-drift delay, but its mean false re-discovery of 0.078 exceeds retraining's 0.033; these outcomes describe distinct aspects of forgetting rather than a single universally fastest method.

Table 4 reports nearly identical checkpoint metrics for the full method and both ablations: nine of ten seeds are identical, and one favours an ablation by 0.010 recall. The reported p=0.317 is not an exact two-sided signed-rank value for one nonzero pair, whose exact p is 1; zero handling and approximation require raw-data reconciliation. Event-sync payload adds 204614 bytes relative to the no-sync variant, about 23.7% of 862360 bytes. The campaign provides no reliable measured improvement from either component at this scale. Distance from the pruning threshold is a possible explanation, not an isolated causal result or a theorem excluding weighting benefits.

Note: Nine pairs are tied; the source p=0.317 requires reconciliation with the stated signed-rank procedure before inferential interpretation.

Table 5 summarizes the same ten-seed campaign. AdaFed-TPM recall ranges from 0.963 to 1.000, and its lowest mean checkpoint recall is 0.950, versus 0.720 for retraining and 0.775 for local adaptation. Reported alarms decrease from 6.20 for the cleanest to 0.50 for the noisiest client, with one intermediate inversion. By the setup, the noisiest client has the highest arrival weight and therefore more, not fewer, transactions. Local batches, baselines, corruption and arrival volume remain confounded; raw alarm traces and a volume-by-corruption factorial design are required to explain the trend. Mean event synchronizations are reported as 23.40 per seed, outside scheduled checkpoint refreshes.

The source reports paired Wilcoxon tests over ten seeds [30], Friedman chi-square(3)=28.6,p=2.7e-06 across four methods [31], and Holm correction across three recall comparisons [32]. The fixed-window p=0.112 supplies no evidence of a difference but does not establish equivalence. The ten random seeds are repeats under one Adult-derived generator and shared planted-change schedule; checkpoints and overlapping windows within a run are temporally dependent, not additional independent samples. The ablation has only one non-tied pair, for which an exact two-sided signed-rank p is 1. The reported p=0.317 remains unresolved until the raw paired values and software settings are supplied.

The reported realization reduces uplink payload relative to fixed-window while having similar observed mean recall, with no significant difference established. It does not show equally accurate performance in a formal equivalence sense. Retraction after the first drift is slower, and second-drift delay ties fixed-window. Ablations establish no measured component improvement at this scale; they do not causally prove that windowing alone generates every observed benefit. H1 has support for payload reduction at one design point, while a general delay or communication guarantee remains open.

The proposed method has the highest dead-pattern re-discovery mean and jointly slowest first-drift mean delay. H2 receives no reliable ablation support, and H3 is untested because the campaign substitutes fixed two-timescale windows for geometric decay. Jaccard stability was not logged. The scope is one Adult-derived generator, a 23-item alphabet, unordered itemsets of size at most three, 10000 transactions, six clients, common planted global drift times, one volume-corruption gradient, ten seeds, no centralized drift-aware oracle, and no privacy layer.

Independent regeneration of the reported campaign requires the original generator and analysis code, exact seeds and partitions, raw checkpoint outputs, message traces, and figure workflow. The manuscript does not identify an accessible versioned release.

Mean-based detection can miss changes in variance, event order or rare-tail combinations. Consensus weighting may suppress legitimate minority populations, stale supports can persist without expiry, and the proposed stability rule does not by itself enforce its floor. Uplink payload accounting omits downlinks and production overhead. The measured trade-off includes higher dead-pattern re-discovery, while privacy, async local drift, geometric decay and ordered episode mining remain untested.

Scheduled refresh provides a simple auditable baseline; event-responsive operation is useful when its savings justify alarm handling and stale-value risk. Regular heartbeats and event responses remain part of the cost. Reliability weighting offers an alternative to exclusion, but agreement-based weights need validation against independent quality evidence and legitimate population differences. Eq. (2) states a design objective rather than a proof that the implemented heuristic prevents trivial stability or satisfies its constraints.

Offline pooled analysis can be a useful alternative when timeliness and data access permit it. Here the simulation evaluates timely distributed refresh at one scale: payload savings are observed, while dead-pattern retraction remains a weakness.