When one time series informs another, the delay at which that information arrives determines if models can utilize this relationship effectively. A source may be strongly predictive at one delay but uninformative at neighboring lags. Therefore, fixed input windows may obscure this structure by bundling informative and irrelevant history together. Transfer entropy (TE) can recover these delays by measuring how much a source's past tells us about a target beyond the target's own history. However, existing TE estimators require separate fits across source and conditioning depths, with further estimation on local windows to track delays over time. We introduce ATEMPO, a diffusion-based transfer entropy estimator amortized over lags and time. ATEMPO samples source and conditioning depths during training and conditions explicitly on temporal position, allowing a single score network to estimate the full TE surface without refitting. Differencing this surface recovers when information arrives. Across synthetic datasets with ground-truth TE, ATEMPO achieves the lowest mean relative error among baselines, and on datasets with known lags, ATEMPO achieves 0.98±0.04 lag-detection accuracy. ATEMPO requires a single fit across source depths K=6 and target depths L=3, whereas existing estimators require 18 separate fits to evaluate the same K×L grid. On three systems with time-varying lag, ATEMPO is the only estimator to maintain perfect lag-detection accuracy across all evaluated window lengths. These recovered delays improve downstream forecasting: ATEMPO-selected inputs reduce MSE on WEATHER-5K by 7.25%, while 120 selected inputs outperform the benchmark's 240-feature default by 4.6%. Across three brain-computer interface tasks, using ATEMPO-selected lags achieves the highest or equal-best R2, improving mean R2 by 4.1% relative to the strongest competing baseline.
Figures & tables
Figure 1: Overview of ATEMPO: During training, source depth k , conditioning depth l and time position t are varied across training samples. A mask m(k,l) specifies which source and target lags are observed, while t and diffusion time τ conditions through the same pathway. After training, the same network is evaluated with and without the source history; the squared difference between the resulting conditional scores estimates TE(k,l,t) . Querying different (k,l,t) recovers the TE surface without refitting, and differencing along k yields the time-varying delay profile. Using these lags as inputs to a forecasting model improves performance over consecutive-timestep baselines.
iTransformer
DLinear
MSE ( ↓ )
Δ vs default ( ↓ )
MSE ( ↓ )
Δ vs default ( ↓ )
selection cost (h)
(a) all 5,672 stations
Default
0.5562
-
0.5840
-
0
ATEMPO
0.5158
-7.25%
0.5252
-10.07%
1.8
(b) 300 stations
Default
0.5223
-
0.5510
-
0
Table 1: Forecasting error on WEATHER-5K at the benchmark’s input size for two forecasters: iTransformer and DLinear. MSE is averaged over the five variables and over training seeds, with standard deviation across seeds <0.002 for every run.
Figure 2: ATEMPO applied to WEATHER5K. a) A delay profile between source variable temperature (TMP) and target variable dew point temperature (DEW) over time, pooled over 300 stations b) The mean delay profile δk=TE(k)−TE(k−1) averaged over 25 variable pairs for each baseline. The darker colors are the lags carrying the most information. c) Forecasting performance (MSE) from using each method’s top ranked n features as inputs.
TE error % (↓)
lag detection: acc. (↑)
lag selection: R2 , 5 lags (↑)
synthetic datasets
synthetic datasets
MMTT- Bench
NLB velocity
NLB decoding
MC_Maze decoding
Mean R2
Liang– Kleeman
-
0.46 ± 0.34
0.00
0.789
0.458
0.582
0.610
DTW
-
0.71 ± 0.42
0.00
0.794
0.402
0.554
0.583
NPEET
56.0 ± 38.7
0.91 ± 0.24
0.33
0.805
0.444
0.504
0.584
PCMI
55.1 ± 22.1
0.92 ± 0.19
1.00
0.794
0.456
0.486
0.579
NJEE
32.9 ± 13.1
0.92 ± 0.13
0.72
0.809
0.402
0.504
0.572
Table 2: Mean relative % error in TE estimation, lag detection accuracy and lag selection forecasting performance ( R2 ) across synthetic and real datasets.
Figure 5
lag detection accuracy ( ↑ )
Relative forecasting error ( ↓ )
samples per window
125
250
500
1000
125
250
500
1000
fitted per window
NPEET
0.68
0.84
0.92
0.92
1.83
1.09
1.05
1.01
NJEE
0.35
0.44
0.62
0.88
2.80
1.83
1.17
1.09
MINE
0.32
0.52
0.67
0.92
3.87
1.28
1.17
1.02
CCMI
0.19
0.42
0.54
0.92
4.70
2.10
1.16
1.00
Table 3: Lag detection and forecasting under a time-varying lag. Results are averaged over three synthetic systems. Lag detection accuracy is the fraction of evaluation windows in which the top-ranked lag equals the true lag. Relative forecasting error is the MSE error compared to the MSE when using true lags for forecasting. Per-window methods are refit independently using only the samples in each window. Fit-once methods are trained on the complete 8,000 sample recording. Only time-conditioned ATEMPO can vary its estimated lag across windows without refitting.
Appendix figures & tables18 assets
Supplementary material from the paper’s appendix.
Appendix
Family
Dataset
Source
Number of
Linear/
Ground
Known
Dimension
true lags
Non-linear
Truth TE
Lag(s)
AGM TE
flat_linear
1
1
linear
( Kornai et al., 2025 )
flat_joint
1
1
non-linear
✓
✓
multi- dimensional
lag_linear_m3_d4
5
1
linear
✓
✓
lag_nonlin_m3_d4
5
1
non-linear
✓
✓
lag_multisource
5
1
linear
✓
✓
Appendix
Table 4: Details of our suite of synthetic datasets with ground truth TE
systems
seeds
cells
sd
sd
Var( δ err) /
corr(err k ,
direction
estimator
TE(k)
δk
(Var k + Var k-1 )
err k-1 )
causal
ATEMPO (one fit)
5
5
75
0.011
0.008
0.286
0.715
TENDE (one fit per cell)
5
5
75
0.019
0.026
0.947
0.053
null
ATEMPO (one fit)
5
5
75
0.001
0.000
0.222
0.782
TENDE (one fit per cell)
5
5
75
0.001
0.001
0.715
0.300
Appendix
Table 5: Do errors in adjacent cells of the TE surface cancel when differenced? Stationary benchmark at K=6 , L=3 , same (system, seed) pairs for both estimators, exact ground truth. Across seeds, per cell: the sd of the TE estimate, the sd of the delay profile δk=TE(k,l)−TE(k−1,l) , the ratio of the variance of the δk error to the sum of the two cell variances (1 for independent errors, below 1 when errors are positively correlated), and the pooled correlation of the two cells’ errors. The null direction has true TE =0 everywhere, so its errors are pure estimation noise.
method
family
NPEET
NJEE
MINE
CCMI
PCMI
TENDE
ATEMPO
system
flat_linear
AGM-TE
6.7 ± 2.3
18.5 ± 4.5
8.5 ± 1.4
5.1 ± 5.2
67.6 ± 2.6
3.9 ± 4.7
6.8 ± 4.1
flat_joint
AGM-TE
2.1 ± 1.7
19.0 ± 3.7
12.1 ± 7.1
2.8 ± 2.5
76.0 ± 1.4
8.7 ± 3.0
9.7 ± 5.2
lag_linear_m3_d4
multi-dimensional
93.1 ± 5.3
38.6 ± 4.7
8.8 ± 4.2
79.4 ± 9.4
27.0 ± 6.3
6.1 ± 2.8
3.7 ± 2.6
lag_multisource
multi-dimensional
44.9 ± 2.7
30.3 ± 5.6
7.4 ± 4.4
20.6 ± 4.5
27.2 ± 4.3
2.5 ± 1.6
4.9 ± 0.9
lag_nonlin_m3_d4
multi-dimensional
81.8 ± 2.1
35.2 ± 3.3
18.8 ± 3.7
8.7 ± 4.0
47.6 ± 2.2
29.6 ± 30.9
9.6 ± 3.0
Appendix
Table 6: Relative error (%) of the TE estimate at the true lag, mean ± sd over 5 seeds. Bold is the lowest error per system.
method
family
true TE
NPEET
NJEE
MINE
CCMI
PCMI
TENDE
ATEMPO
system
flat_linear
AGM-TE
0.128
-0.6 ± 7.8
-18.5 ± 4.5
2.1 ± 9.3
-1.9 ± 7.5
-67.6 ± 2.6
-3.3 ± 5.3
2.3 ± 8.3
flat_joint
AGM-TE
0.415
-0.7 ± 2.8
-19.0 ± 3.7
-12.1 ± 7.1
-2.0 ± 3.3
-76.0 ± 1.4
-8.7 ± 3.0
-9.1 ± 6.3
lag_linear_m3_d4
multi-dim.
0.128
-93.1 ± 5.3
-38.6 ± 4.7
8.8 ± 4.2
79.4 ± 9.4
-27.0 ± 6.3
-6.1 ± 2.8
1.5 ± 4.6
lag_multisource
multi-dim.
0.128
-44.9 ± 2.7
-30.3 ± 5.6
-6.3 ± 6.2
20.6 ± 4.5
-27.2 ± 4.3
0.5 ± 3.2
2.9 ± 4.6
lag_nonlin_m3_d4
multi-dim.
0.415
-81.8 ± 2.1
-35.2 ± 3.3
-18.8 ± 3.7
8.7 ± 4.0
-47.6 ± 2.2
-29.6 ± 30.9
-9.6 ± 3.0
Appendix
Table 7: Signed relative error (%) at the true lag (negative = under-estimate), mean ± sd over seeds.
family
system
trials
NPEET
NJEE
MINE
CCMI
PCMI
Liang
DTW
TENDE
ATEMPO
-Kleeman
AGM-TE
flat_linear
seeds
5/5
5/5
5/5
5/5
5/5
5/5
5/5
5/5
5/5
flat_joint
seeds
5/5
5/5
5/5
5/5
5/5
2/5
5/5
5/5
5/5
multi- dimensional
lag_linear_m3d4
seeds
1/5
5/5
5/5
5/5
5/5
5/5
5/5
5/5
5/5
lag_multisource
seeds
5/5
5/5
5/5
5/5
5/5
3/5
5/5
5/5
5/5
lag_nonlin_m3d4
seeds
5/5
5/5
5/5
5/5
5/5
3/5
5/5
5/5
5/5
Appendix
Table 8: Top-1 lag recovery (successes / trials) on every synthetic system. Stationary systems: one trial per seed; time-varying systems: one trial per 1000-sample window.
switch
switch_sq
switch_sq_wk
win_len
125
250
500
1000
125
250
500
1000
125
250
500
1000
Liang- Kleeman
0.39
0.38
0.44
0.38
0.17
0.19
0.12
0.12
0.14
0.03
0.12
0.25
NPEET
0.67
0.84
0.94
1.00
0.95
1.00
1.00
1.00
0.42
0.69
0.81
0.75
NJEE
0.19
0.25
0.69
0.88
0.69
0.88
1.00
1.00
0.17
0.19
0.19
0.75
MINE
0.22
0.41
0.69
1.00
0.61
0.94
0.94
1.00
0.12
0.22
0.38
0.75
CCMI
0.03
0.03
0.06
0.88
0.44
0.88
1.00
1.00
0.09
0.34
0.56
0.88
Appendix
Table 9: Top-1 detection rate on a moving lag against samples per window, per system and averaged. Baselines are re-fitted in every window; ATEMPO is fitted once.
switch
switch_sq
switch_sq_wk
win_len
125
250
500
1000
125
250
500
1000
125
250
500
1000
NPEET
0.224
0.228
0.208
0.209
0.313
0.099
0.099
0.099
0.117
0.111
0.108
0.097
NJEE
0.257
0.256
0.249
0.210
0.578
0.292
0.099
0.099
0.124
0.122
0.122
0.117
MINE
0.251
0.244
0.248
0.209
0.899
0.132
0.114
0.099
0.123
0.126
0.111
0.098
CCMI
0.258
0.259
0.258
0.208
1.142
0.372
0.099
0.099
0.122
0.121
0.117
0.093
PCMI
0.257
0.260
0.279
0.208
1.226
0.402
0.099
0.099
0.122
0.124
0.122
0.116
Appendix
Table 10: Ablation arms: forecasting MSE against window length, per system.
m=1
m=2
m=3
m=4
m=5
m=6
mean
shuffled
time rel.
method
(null)
ATEMPO
Liang- Kleeman
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.940
0.000
DTW
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.890
0.000
NPEET
1.000
0.000
0.000
1.000
0.000
0.000
0.330
0.890
0.050
NJEE
1.000
0.330
1.000
1.000
0.330
0.670
0.720
0.940
0.550
MINE
1.000
0.330
1.000
1.000
1.000
0.670
0.830
0.940
1.330
Appendix
Table 11: MMTT-Bench lag recovery per planted delay (3 seeds), null rejection on shuffled text, and cost relative to ATEMPO.
ATEMPO estimates
% MSE
condition
TE (nats)
peak δ TE
lag found
default (lag 1)
atempo lag
random lag
correct
0.52
0.27
1.00
15.59
41.26
10.37
incorrect
0.21
0.05
0.00
7.89
1.09
3.12
irrelevant
0.14
0.05
0.00
-0.69
-2.35
-1.32
shuffled
0.15
0.05
0.00
-1.50
-1.18
-1.19
Appendix
Table 12: MMTT-Bench by text condition, averaged over planted delays m∈{1−6} and 3 seeds. Left: what ATEMPO estimates. Right: % MSE reduction over forecasting the signal from its own past alone, when one text lag is added: the benchmark’s default lag 1, the lag ATEMPO selects, and a random lag. Only correct text carries a lag to find; on the three controls no choice of lag helps.
temp.
dew
wind
wind
pres-
MSE
sd
Δ
inputs
n feat.
point
dir.
speed
sure
norm.
norm.
(%)
matched (67)
Random
40
20.9
21.6
9086
5.04
53.8
0.507
0.008
1.17
60
19.4
20.9
8956
4.87
52.4
0.494
0.006
-1.51
80
18.7
20.5
8869
4.79
51.4
0.486
0.006
-3.07
120
18.3
20.3
8800
4.71
51.3
0.481
0.004
-3.97
Appendix
Table 13: WEATHER-5K, results using ridge forecaster model on the 300-station subset, reported as MSE per variable for every lag selector, candidate pool and budget. Random rows are means over n=20 draws with the sd of the normalized metric. Δ is against the 48 h default (240 features).
steps
selection
train
temp.
dew
wind
wind
pressure
MSE
Δ
inputs
n feat.
seed
(x1000)
(h)
(min)
point
dir.
speed
norm.
(%)
(a) all 5,672 stations
ATEMPO
240
2021
300
1.787
79
18.373
21.828
8830.489
5.180
59.022
0.516
-7.254
Default (48 h)
240
2021
300
0.000
110
20.406
24.516
9374.630
5.613
63.687
0.556
0.000
(b) 300 stations
ATEMPO
240
2021
200
1.787
79
16.959
19.999
8672.705
4.559
58.924
0.491
-5.951
Appendix
Table 14: WEATHER-5K, iTransformer, test MSE per variable in original units (pred_len 168). ‘MSE norm.’ is the benchmark’s scaled-space metric; Δ is its % change against the 48 h default of the same station set.
persis
sub-
diurnal
synoptic
weekly
boundary
phase
median
budget
selector
-tence
daily
R
lag (h)
24
Default
3
19
2
0
0
0
0.00
12.50
Random
0
2
0
21
1
0
0.29
162.00
PCMI
1
3
13
6
0
1
0.35
114.00
NPEET
2
13
1
8
0
0
0.11
17.50
MINE
0
0
2
20
2
0
0.20
154.50
Appendix
Table 15: Where each selector spends its feature budget: the lag sets the iTransformer arms were trained on, counted by band. Default refers to the most recent n= budget lags.
n lags
cost of
per lag
per lag
per lag
budget
band
band (%)
(band)
(LOO mean)
(LOO max)
24
persistence
2
1.54
0.77
0.30
0.55
sub-daily
7
1.42
0.20
0.05
0.11
diurnal
3
0.43
0.14
0.11
0.12
synoptic
4
1.18
0.30
0.20
0.33
weekly
1
0.86
0.86
0.86
0.86
Appendix
Table 16: Which of ATEMPO’s selected lags do the forecasting work. Ridge on 300 stations, scored using mean MSE over variables. Each band row removes that band from ATEMPO’s set and reports the % change of the metric relative to the full set: a positive cost of band means the forecast got worse without it, i.e. the band was helping; per lag (band) divides by the band’s size, and the leave-one-out (LOO) columns give the mean and the largest change from removing a single lag of the band.
iTransformer
DLinear
PatchTST
Pyraformer
Chronos-2 †
MSE ( ↓ )
Δ(↓)
MSE ( ↓ )
Δ(↓)
MSE ( ↓ )
Δ(↓)
MSE ( ↓ )
Δ(↓)
MSE ( ↓ )
Δ(↓)
Default
0.5223 ± 0.0007
-
0.5510 < 0.0001
-
0.5480 < 0.0001
-
0.4689
-
0.6478
-
Random
0.5066 ± 0.0016
-3.00%
0.5040 < 0.0001
-8.53%
0.5004 ± 0.0002
-8.69%
0.4901
+4.52%
0.6351
-1.96%
CCMI
0.4904 ± 0.0009
-6.10%
0.4917 < 0.0001
-10.77%
0.4859 ± 0.0006
-11.33%
0.4748
+1.26%
0.5959
-8.01%
ATEMPO
0.4904 ± 0.0014
-6.10%
0.4948 < 0.0001
-10.21%
0.4879 ± 0.0009
-10.97%
0.4774
+1.82%
0.6239
-3.69%
Default > Random > CCMI, ATEMPO
✓
✓
✓
× (default best)
✓
Appendix
Table 17: WEATHER-5K at the benchmark’s input size (48 selected lags, 300 stations) for five forecaster families, testing whether the ordering of Table 1 (default > random > the two strongest selectors) depends on the forecaster or on the input layout. MSE is averaged over the five variables and over training seeds ( ± sd across seeds where more than one; < 0.0001 where smaller); Δ is the percentage change against the default of the same panel. The check row marks whether the ordering holds. The last row gives every model the full 336 h window, Δ against the default.
iTransformer
DLinear
lags
selector
seeds
MSE norm.
Δ (%)
seeds
MSE norm.
Δ (%)
48
Default
3
0.522
0.0
3
0.551
0.0
Random
3
0.507
-3.0
3
0.504
-8.5
ATEMPO
5
0.490
-6.1
3
0.495
-10.2
CCMI
5
0.490
-6.1
3
0.492
-10.8
NJEE
3
0.497
-4.8
3
0.497
-9.9
Appendix
Table 18: Every lag set of the paper’s grid under the two architectures that take gathered inputs unchanged. Normalized MSE, mean over seeds, and % change against each model’s own 48 h default (300 stations). Spearman rank correlation of the two columns across selectors: 0.82 at 48 lags ( n=10 ), 0.88 at 24 lags ( n=8 ).
additional lags
NLB velocity
NLB decoding
MC_Maze decoding
chosen by
+1
+2
+3
+5
+1
+2
+3
+5
+1
+2
+3
+5
ATEMPO
0.699
0.728
0.755
0.812
0.246
0.305
0.336
0.474
0.356
0.518
0.557
0.619
cross-correlation
0.727
0.754
0.755
0.794
0.382
0.400
0.425
0.448
0.359
0.395
0.449
0.504
most recent lags
0.699
0.728
0.755
0.794
0.246
0.305
0.336
0.402
0.356
0.394
0.453
0.504
evenly spaced
0.699
0.699
0.699
0.792
0.246
0.267
0.384
0.468
0.356
0.441
0.552
0.626
random
0.717
0.737
0.762
0.790
0.345
0.375
0.415
0.448
0.332
0.432
0.515
0.580
Appendix
Table 19: Lag budgets on the three NLB tasks. For NLB velocity and decoding, forecasting input is lag 0 plus B selected input lags. For MC_Maze there is no base input, only B selected lag bins. R2 calculated on held-out validation split.
ATEMPO
ChronoEpilogi
GroupLasso
NoSelection
own past
dataset
Electricity
0.901 (30)
0.899 (24)
0.900 (36)
0.824 (320)
0.882
METR-LA
0.885 (2)
0.884 (1)
0.883 (4)
0.178 (206)
0.884
Solar
0.989 (13)
0.990 (10)
0.990 (10)
0.988 (136)
0.988
PEMS-BAY
0.925 (4)
0.927 (5)
0.927 (8)
-0.831 (324)
0.927
Traffic †
0.710 (13)
0.842 (13)
0.792 (38)
-1.048 (861)
0.787
Appendix
Table 20: Comparison to ChronoEpilogi results: test R2 of the ridge forecaster (mean over the 10 targets) with, in parentheses, the number of series each method keeps when choosing its own size on a validation split of the training part; NoSelection uses all series, and the last column is the target’s own past alone. † Traffic’s test period is nonstationary; see the appendix.
Figure 5: All five datasets: median ridge test R2 against the number of selected series B , by selector (the greedy wrapper is omitted; dotted line = the target’s own past only). Note the vertical scales differ by panel: the three saturated datasets span a few thousandths of R2 .
Attention mechanisms are effective for multivariate time series modeling because they adaptively aggregate information across timestamps and variables. Their quadratic cost, however, limits their use in multivariate and spatio-temporal systems. Linear attention reduces this cost by replacing nonlinear attention mappings with forms that support associative computation. Replacing exponential weighting may weaken the amplification of high-score positions and further bias weakly selective distributions toward uniform aggregation. We propose an entropy-calibrated linear attention module and instantiate it as the ELinFormer forecaster. Our operator decomposes aggregation into a uniform component and a query-dependent correction, whose magnitude is calibrated by a query-specific temperature. We derive a second-order KL proxy from centered query-key scores. The Taylor expansion reduces the proxy to the squared-score energy divided by the squared temperature. This score energy can be computed from shared products of the centered keys without forming the full pairwise score matrix, and the same products support the linear attention output. We design a smooth temperature rule to calibrate the KL proxy: it keeps low-energy residuals vanishing, approximately calibrates moderate-energy queries to a shared KL level, and allows the proxy to continue growing for high-energy queries. Experiments on five PEMS benchmarks show competitive forecasting accuracy. Controlled comparisons with vanilla attention and Linformer demonstrate a favorable accuracy--memory trade-off, while analysis on PEMS08 shows that the proposed rational temperature rule and query-specific calibration achieve lower MAE than a linear rule or shared-temperature alternatives. These results support entropy calibration as an effective mechanism for preserving selective deviations in linear attention.
Mingtao Zhang, Guoli Yang, Zhanxing Zhu +2
Advanced Institute of Big Data, Beijing · University of Southampton
Time series forecasting models are increasingly scaled through large Transformer backbones, yet most existing approaches process all series through a shared dense computation path despite substantial heterogeneity in temporal structure. Mixture-of-Experts (MoE) offers a natural alternative by enabling conditional computation, but standard MoE routing leaves expert specialization weakly identified and often unstable during downstream adaptation. We propose AME-TS, a structure-guided sparse time series foundation model that aligns expert routing with interpretable temporal structure. AME-TS first uses a lightweight regime predictor to estimate series-level descriptors, including forecastability, seasonality, trend, and sparsity, and maps them to a soft structural prior over experts. This series-level prior guides token-level routing during training, encouraging structure-aligned specialization. On the GIFT-Eval benchmark, AME-TS delivers a strong accuracy-efficiency tradeoff across model scales: it substantially outperforms existing time series foundation models at small model scales and remains competitive with the strongest models at larger scales, while activating substantially fewer parameters through sparse routing. We further show that AME-TS learns more interpretable routing geometry and substantially more stable expert specialization than standard MoE during fine-tuning on the M5 dataset. These results suggest that structure-aware routing is an effective and reliable way to realize the benefits of sparse expert models for time series forecasting.
Event-Based Models (EBMs) infer biomarker progression from cross-sectional data but typically only as ordinal sequences and rely on rigid model assumptions. We propose Tempo, a Transformer architecture that learns both ordinal and continuous event sequences through simulation-based supervised learning. Tempo uses two Transformer modules: one treats biomarkers as tokens to infer event sequencing; the other treats patients as tokens, representing each by their per-biomarker abnormality profile, to infer patients' disease stages. On synthetic benchmarks, Tempo reduces normalized Kendall's Tau distance by 52.89% and staging MAE by 25.33% compared to state-of-the-art SA-EBM, with larger reductions in high-dimensional settings (58.88% and 61.10%). Applied to ADNI, Tempo recovers a biologically plausible Alzheimer's progression: early medial temporal atrophy, followed by amyloid accumulation and cognitive decline, and late-stage tau pathology with terminal acceleration of global neurodegeneration -- broadly consistent with established disease models. Tempo also eliminates the need to derive custom inference algorithms and enables rapid empirical comparison of generative hypotheses.
Hongtao Hao, Joseph L. Austerweil
University of Wisconsin—Madison, USA · Chiba Institute of Technology, Japan & University of Wisconsin—Madison, USA