Poisson SLDS
Note
Click here to download the full example code
Poisson SLDS#
Fitting SLDS with BBVI
0%| | 0/1000 [00:00<?, ?it/s]
LP: -105245.2: 0%| | 0/1000 [00:00<?, ?it/s]
ELBO: -105243.8: 0%| | 0/1000 [00:00<?, ?it/s]
ELBO: -105177.8: 0%| | 1/1000 [00:00<02:29, 6.69it/s]
ELBO: -105177.8: 0%| | 2/1000 [00:00<01:14, 13.37it/s]
ELBO: -105177.6: 0%| | 4/1000 [00:00<01:14, 13.37it/s]
ELBO: -105079.7: 0%| | 5/1000 [00:00<01:14, 13.37it/s]
ELBO: -105079.7: 1%| | 6/1000 [00:00<00:38, 25.88it/s]
ELBO: -104971.6: 1%| | 6/1000 [00:00<00:38, 25.88it/s]
ELBO: -104924.1: 1%|1 | 10/1000 [00:00<00:38, 25.88it/s]
ELBO: -104924.1: 1%|1 | 11/1000 [00:00<00:30, 32.10it/s]
ELBO: -104905.0: 1%|1 | 11/1000 [00:00<00:30, 32.10it/s]
ELBO: -104876.4: 1%|1 | 12/1000 [00:00<00:30, 32.10it/s]
ELBO: -104747.4: 1%|1 | 13/1000 [00:00<00:30, 32.10it/s]
ELBO: -104729.1: 1%|1 | 14/1000 [00:00<00:30, 32.10it/s]
ELBO: -104729.1: 2%|1 | 15/1000 [00:00<00:44, 22.30it/s]
ELBO: -104702.4: 2%|1 | 19/1000 [00:00<00:43, 22.30it/s]
ELBO: -104718.9: 2%|2 | 20/1000 [00:00<00:43, 22.30it/s]
ELBO: -104648.6: 2%|2 | 21/1000 [00:00<00:43, 22.30it/s]
ELBO: -104648.6: 2%|2 | 22/1000 [00:00<00:29, 33.35it/s]
ELBO: -104642.2: 2%|2 | 22/1000 [00:00<00:29, 33.35it/s]
ELBO: -104584.4: 2%|2 | 23/1000 [00:00<00:29, 33.35it/s]
ELBO: -104522.4: 2%|2 | 24/1000 [00:00<00:29, 33.35it/s]
ELBO: -104574.2: 2%|2 | 25/1000 [00:00<00:29, 33.35it/s]
ELBO: -104502.4: 3%|2 | 26/1000 [00:00<00:29, 33.35it/s]
ELBO: -104502.4: 3%|2 | 27/1000 [00:00<00:35, 27.24it/s]
ELBO: -104473.4: 3%|2 | 27/1000 [00:01<00:35, 27.24it/s]
ELBO: -104459.1: 3%|3 | 32/1000 [00:01<00:35, 27.24it/s]
ELBO: -104459.1: 3%|3 | 33/1000 [00:01<00:30, 31.65it/s]
ELBO: -104420.5: 3%|3 | 33/1000 [00:01<00:30, 31.65it/s]
ELBO: -104358.4: 3%|3 | 34/1000 [00:01<00:30, 31.65it/s]
ELBO: -104372.1: 4%|3 | 35/1000 [00:01<00:30, 31.65it/s]
ELBO: -104350.2: 4%|3 | 36/1000 [00:01<00:30, 31.65it/s]
ELBO: -104350.2: 4%|3 | 37/1000 [00:01<00:30, 31.72it/s]
ELBO: -104318.4: 4%|3 | 37/1000 [00:01<00:30, 31.72it/s]
ELBO: -104299.3: 4%|3 | 38/1000 [00:01<00:30, 31.72it/s]
ELBO: -104244.3: 4%|3 | 39/1000 [00:01<00:30, 31.72it/s]
ELBO: -104226.6: 4%|4 | 40/1000 [00:01<00:30, 31.72it/s]
ELBO: -104226.6: 4%|4 | 41/1000 [00:01<00:35, 27.00it/s]
ELBO: -104228.5: 4%|4 | 41/1000 [00:01<00:35, 27.00it/s]
ELBO: -104216.8: 4%|4 | 42/1000 [00:01<00:35, 27.00it/s]
ELBO: -104148.9: 4%|4 | 43/1000 [00:01<00:35, 27.00it/s]
ELBO: -104148.9: 5%|4 | 48/1000 [00:01<00:31, 30.44it/s]
ELBO: -104223.5: 5%|4 | 48/1000 [00:01<00:31, 30.44it/s]
ELBO: -104164.5: 5%|4 | 49/1000 [00:01<00:31, 30.44it/s]
ELBO: -104188.8: 5%|5 | 50/1000 [00:01<00:31, 30.44it/s]
ELBO: -104113.8: 5%|5 | 51/1000 [00:01<00:31, 30.44it/s]
ELBO: -104113.8: 5%|5 | 52/1000 [00:01<00:36, 26.30it/s]
ELBO: -104121.3: 5%|5 | 52/1000 [00:01<00:36, 26.30it/s]
ELBO: -104096.6: 5%|5 | 53/1000 [00:02<00:36, 26.30it/s]
ELBO: -104013.3: 5%|5 | 54/1000 [00:02<00:35, 26.30it/s]
ELBO: -104013.3: 6%|5 | 55/1000 [00:02<00:41, 22.74it/s]
ELBO: -104037.2: 6%|5 | 55/1000 [00:02<00:41, 22.74it/s]
ELBO: -104051.0: 6%|5 | 56/1000 [00:02<00:41, 22.74it/s]
ELBO: -104071.6: 6%|5 | 57/1000 [00:02<00:41, 22.74it/s]
ELBO: -104071.6: 6%|5 | 58/1000 [00:02<00:39, 23.60it/s]
ELBO: -104033.9: 6%|5 | 58/1000 [00:02<00:39, 23.60it/s]
ELBO: -103931.3: 6%|5 | 59/1000 [00:02<00:39, 23.60it/s]
ELBO: -103979.7: 6%|6 | 60/1000 [00:02<00:39, 23.60it/s]
ELBO: -103979.7: 6%|6 | 61/1000 [00:02<00:49, 19.13it/s]
ELBO: -104001.1: 6%|6 | 61/1000 [00:02<00:49, 19.13it/s]
ELBO: -103973.1: 6%|6 | 62/1000 [00:02<00:49, 19.13it/s]
ELBO: -103871.8: 6%|6 | 63/1000 [00:02<00:48, 19.13it/s]
ELBO: -103871.8: 6%|6 | 64/1000 [00:02<00:57, 16.30it/s]
ELBO: -103958.0: 6%|6 | 64/1000 [00:02<00:57, 16.30it/s]
ELBO: -103878.4: 6%|6 | 65/1000 [00:02<00:57, 16.30it/s]
ELBO: -103878.4: 7%|6 | 66/1000 [00:02<00:59, 15.63it/s]
ELBO: -103958.9: 7%|6 | 66/1000 [00:02<00:59, 15.63it/s]
ELBO: -103865.3: 7%|6 | 69/1000 [00:02<00:59, 15.63it/s]
ELBO: -103865.3: 7%|7 | 70/1000 [00:02<00:46, 19.97it/s]
ELBO: -103886.0: 7%|7 | 70/1000 [00:02<00:46, 19.97it/s]
ELBO: -103818.5: 7%|7 | 71/1000 [00:03<00:46, 19.97it/s]
ELBO: -103855.9: 7%|7 | 72/1000 [00:03<00:46, 19.97it/s]
ELBO: -103855.9: 7%|7 | 73/1000 [00:03<00:45, 20.18it/s]
ELBO: -103845.9: 7%|7 | 73/1000 [00:03<00:45, 20.18it/s]
ELBO: -103768.8: 7%|7 | 74/1000 [00:03<00:45, 20.18it/s]
ELBO: -103779.7: 8%|7 | 75/1000 [00:03<00:45, 20.18it/s]
ELBO: -103779.7: 8%|7 | 76/1000 [00:03<00:53, 17.41it/s]
ELBO: -103806.5: 8%|7 | 76/1000 [00:03<00:53, 17.41it/s]
ELBO: -103725.0: 8%|7 | 77/1000 [00:03<00:53, 17.41it/s]
ELBO: -103725.0: 8%|7 | 78/1000 [00:03<00:56, 16.29it/s]
ELBO: -103781.4: 8%|7 | 78/1000 [00:03<00:56, 16.29it/s]
ELBO: -103721.7: 8%|7 | 79/1000 [00:03<00:56, 16.29it/s]
ELBO: -103777.7: 8%|8 | 80/1000 [00:03<00:56, 16.29it/s]
ELBO: -103777.7: 8%|8 | 81/1000 [00:03<00:56, 16.25it/s]
ELBO: -103686.1: 8%|8 | 81/1000 [00:03<00:56, 16.25it/s]
ELBO: -103744.0: 8%|8 | 82/1000 [00:03<00:56, 16.25it/s]
ELBO: -103753.3: 8%|8 | 83/1000 [00:03<00:56, 16.25it/s]
ELBO: -103730.2: 8%|8 | 84/1000 [00:03<00:56, 16.25it/s]
ELBO: -103730.2: 8%|8 | 85/1000 [00:03<00:48, 18.92it/s]
ELBO: -103760.7: 8%|8 | 85/1000 [00:03<00:48, 18.92it/s]
ELBO: -103732.3: 9%|8 | 86/1000 [00:03<00:48, 18.92it/s]
ELBO: -103732.3: 9%|8 | 87/1000 [00:03<00:49, 18.33it/s]
ELBO: -103713.2: 9%|8 | 89/1000 [00:03<00:49, 18.33it/s]
ELBO: -103729.0: 9%|9 | 90/1000 [00:04<00:49, 18.33it/s]
ELBO: -103729.0: 9%|9 | 91/1000 [00:04<00:42, 21.14it/s]
ELBO: -103679.8: 9%|9 | 91/1000 [00:04<00:42, 21.14it/s]
ELBO: -103629.7: 9%|9 | 92/1000 [00:04<00:42, 21.14it/s]
ELBO: -103588.5: 9%|9 | 93/1000 [00:04<00:42, 21.14it/s]
ELBO: -103588.5: 9%|9 | 94/1000 [00:04<00:44, 20.32it/s]
ELBO: -103731.4: 9%|9 | 94/1000 [00:04<00:44, 20.32it/s]
ELBO: -103584.5: 10%|9 | 95/1000 [00:04<00:44, 20.32it/s]
ELBO: -103604.7: 10%|9 | 96/1000 [00:04<00:44, 20.32it/s]
ELBO: -103604.7: 10%|9 | 97/1000 [00:04<00:46, 19.52it/s]
ELBO: -103617.8: 10%|9 | 97/1000 [00:04<00:46, 19.52it/s]
ELBO: -103596.1: 10%|9 | 98/1000 [00:04<00:46, 19.52it/s]
ELBO: -103596.1: 10%|9 | 99/1000 [00:04<00:47, 18.78it/s]
ELBO: -103600.7: 10%|9 | 99/1000 [00:04<00:47, 18.78it/s]
ELBO: -103563.6: 10%|# | 100/1000 [00:04<00:47, 18.78it/s]
ELBO: -103563.6: 10%|# | 101/1000 [00:04<00:50, 17.76it/s]
ELBO: -103516.3: 10%|# | 101/1000 [00:04<00:50, 17.76it/s]
ELBO: -103559.9: 10%|# | 102/1000 [00:04<00:50, 17.76it/s]
ELBO: -103517.5: 10%|# | 103/1000 [00:04<00:50, 17.76it/s]
ELBO: -103517.5: 10%|# | 104/1000 [00:04<00:44, 20.30it/s]
ELBO: -103498.3: 10%|# | 104/1000 [00:04<00:44, 20.30it/s]
ELBO: -103527.7: 10%|# | 105/1000 [00:04<00:44, 20.30it/s]
ELBO: -103514.8: 11%|# | 106/1000 [00:04<00:44, 20.30it/s]
ELBO: -103514.8: 11%|# | 107/1000 [00:04<00:46, 19.30it/s]
ELBO: -103528.4: 11%|# | 107/1000 [00:04<00:46, 19.30it/s]
ELBO: -103499.0: 11%|# | 108/1000 [00:05<00:46, 19.30it/s]
ELBO: -103492.2: 11%|# | 109/1000 [00:05<00:46, 19.30it/s]
ELBO: -103492.2: 11%|#1 | 110/1000 [00:05<00:50, 17.59it/s]
ELBO: -103472.3: 11%|#1 | 112/1000 [00:05<00:50, 17.59it/s]
ELBO: -103464.3: 11%|#1 | 113/1000 [00:05<00:50, 17.59it/s]
ELBO: -103432.2: 11%|#1 | 114/1000 [00:05<00:50, 17.59it/s]
ELBO: -103432.2: 12%|#1 | 115/1000 [00:05<00:37, 23.36it/s]
ELBO: -103474.2: 12%|#1 | 115/1000 [00:05<00:37, 23.36it/s]
ELBO: -103468.2: 12%|#1 | 116/1000 [00:05<00:37, 23.36it/s]
ELBO: -103461.7: 12%|#1 | 117/1000 [00:05<00:37, 23.36it/s]
ELBO: -103461.7: 12%|#1 | 118/1000 [00:05<00:44, 20.00it/s]
ELBO: -103411.9: 12%|#1 | 118/1000 [00:05<00:44, 20.00it/s]
ELBO: -103485.3: 12%|#1 | 119/1000 [00:05<00:44, 20.00it/s]
ELBO: -103426.4: 12%|#2 | 120/1000 [00:05<00:43, 20.00it/s]
ELBO: -103426.4: 12%|#2 | 121/1000 [00:05<00:47, 18.52it/s]
ELBO: -103386.3: 12%|#2 | 121/1000 [00:05<00:47, 18.52it/s]
ELBO: -103420.4: 12%|#2 | 122/1000 [00:05<00:47, 18.52it/s]
ELBO: -103377.5: 12%|#2 | 123/1000 [00:05<00:47, 18.52it/s]
ELBO: -103377.5: 12%|#2 | 124/1000 [00:05<00:43, 20.25it/s]
ELBO: -103304.6: 12%|#2 | 124/1000 [00:05<00:43, 20.25it/s]
ELBO: -103339.4: 12%|#2 | 125/1000 [00:05<00:43, 20.25it/s]
ELBO: -103277.7: 13%|#2 | 126/1000 [00:05<00:43, 20.25it/s]
ELBO: -103277.7: 13%|#2 | 127/1000 [00:05<00:46, 18.63it/s]
ELBO: -103315.2: 13%|#2 | 127/1000 [00:06<00:46, 18.63it/s]
ELBO: -103347.1: 13%|#2 | 128/1000 [00:06<00:46, 18.63it/s]
ELBO: -103340.0: 13%|#2 | 129/1000 [00:06<00:46, 18.63it/s]
ELBO: -103340.0: 13%|#3 | 130/1000 [00:06<00:49, 17.45it/s]
ELBO: -103313.8: 13%|#3 | 130/1000 [00:06<00:49, 17.45it/s]
ELBO: -103272.8: 13%|#3 | 131/1000 [00:06<00:49, 17.45it/s]
ELBO: -103255.1: 13%|#3 | 132/1000 [00:06<00:49, 17.45it/s]
ELBO: -103255.1: 13%|#3 | 133/1000 [00:06<00:44, 19.43it/s]
ELBO: -103284.9: 13%|#3 | 133/1000 [00:06<00:44, 19.43it/s]
ELBO: -103247.2: 13%|#3 | 134/1000 [00:06<00:44, 19.43it/s]
ELBO: -103259.2: 14%|#3 | 135/1000 [00:06<00:44, 19.43it/s]
ELBO: -103259.2: 14%|#3 | 136/1000 [00:06<00:45, 19.20it/s]
ELBO: -103221.6: 14%|#3 | 139/1000 [00:06<00:44, 19.20it/s]
ELBO: -103279.5: 14%|#4 | 140/1000 [00:06<00:44, 19.20it/s]
ELBO: -103202.2: 14%|#4 | 141/1000 [00:06<00:44, 19.20it/s]
ELBO: -103202.2: 14%|#4 | 142/1000 [00:06<00:33, 25.49it/s]
ELBO: -103240.7: 14%|#4 | 142/1000 [00:06<00:33, 25.49it/s]
ELBO: -103276.6: 14%|#4 | 143/1000 [00:06<00:33, 25.49it/s]
ELBO: -103165.3: 14%|#4 | 144/1000 [00:06<00:33, 25.49it/s]
ELBO: -103165.3: 14%|#4 | 145/1000 [00:06<00:35, 24.34it/s]
ELBO: -103199.8: 14%|#4 | 145/1000 [00:06<00:35, 24.34it/s]
ELBO: -103268.3: 15%|#4 | 146/1000 [00:06<00:35, 24.34it/s]
ELBO: -103161.5: 15%|#4 | 147/1000 [00:06<00:35, 24.34it/s]
ELBO: -103161.5: 15%|#4 | 148/1000 [00:06<00:37, 22.59it/s]
ELBO: -103154.7: 15%|#4 | 148/1000 [00:06<00:37, 22.59it/s]
ELBO: -103122.7: 15%|#4 | 149/1000 [00:07<00:37, 22.59it/s]
ELBO: -103143.0: 15%|#5 | 150/1000 [00:07<00:37, 22.59it/s]
ELBO: -103143.0: 15%|#5 | 151/1000 [00:07<00:40, 20.79it/s]
ELBO: -103149.5: 15%|#5 | 151/1000 [00:07<00:40, 20.79it/s]
ELBO: -103157.2: 15%|#5 | 152/1000 [00:07<00:40, 20.79it/s]
ELBO: -103151.2: 15%|#5 | 153/1000 [00:07<00:40, 20.79it/s]
ELBO: -103151.2: 15%|#5 | 154/1000 [00:07<00:39, 21.26it/s]
ELBO: -103188.0: 15%|#5 | 154/1000 [00:07<00:39, 21.26it/s]
ELBO: -103095.4: 16%|#5 | 155/1000 [00:07<00:39, 21.26it/s]
ELBO: -103123.0: 16%|#5 | 156/1000 [00:07<00:39, 21.26it/s]
ELBO: -103123.0: 16%|#5 | 157/1000 [00:07<00:39, 21.20it/s]
ELBO: -103089.3: 16%|#5 | 157/1000 [00:07<00:39, 21.20it/s]
ELBO: -103082.2: 16%|#5 | 158/1000 [00:07<00:39, 21.20it/s]
ELBO: -103101.9: 16%|#5 | 159/1000 [00:07<00:39, 21.20it/s]
ELBO: -103101.9: 16%|#6 | 160/1000 [00:07<00:39, 21.28it/s]
ELBO: -103054.6: 16%|#6 | 160/1000 [00:07<00:39, 21.28it/s]
ELBO: -103029.9: 16%|#6 | 161/1000 [00:07<00:39, 21.28it/s]
ELBO: -103026.9: 16%|#6 | 162/1000 [00:07<00:39, 21.28it/s]
ELBO: -103026.9: 16%|#6 | 163/1000 [00:07<00:44, 18.81it/s]
ELBO: -103085.8: 16%|#6 | 163/1000 [00:07<00:44, 18.81it/s]
ELBO: -103026.5: 17%|#6 | 166/1000 [00:07<00:44, 18.81it/s]
ELBO: -103026.5: 17%|#6 | 167/1000 [00:07<00:38, 21.90it/s]
ELBO: -103028.1: 17%|#6 | 167/1000 [00:07<00:38, 21.90it/s]
ELBO: -102995.1: 17%|#6 | 168/1000 [00:07<00:37, 21.90it/s]
ELBO: -103022.7: 17%|#6 | 169/1000 [00:07<00:37, 21.90it/s]
ELBO: -103022.7: 17%|#7 | 170/1000 [00:07<00:38, 21.84it/s]
ELBO: -103034.6: 17%|#7 | 170/1000 [00:07<00:38, 21.84it/s]
ELBO: -102964.6: 17%|#7 | 171/1000 [00:08<00:37, 21.84it/s]
ELBO: -103037.4: 17%|#7 | 172/1000 [00:08<00:37, 21.84it/s]
ELBO: -103037.4: 17%|#7 | 173/1000 [00:08<00:39, 20.70it/s]
ELBO: -102934.4: 17%|#7 | 173/1000 [00:08<00:39, 20.70it/s]
ELBO: -102998.0: 17%|#7 | 174/1000 [00:08<00:39, 20.70it/s]
ELBO: -102962.1: 18%|#7 | 175/1000 [00:08<00:39, 20.70it/s]
ELBO: -102962.1: 18%|#7 | 176/1000 [00:08<00:38, 21.27it/s]
ELBO: -102980.7: 18%|#7 | 176/1000 [00:08<00:38, 21.27it/s]
ELBO: -102966.8: 18%|#7 | 177/1000 [00:08<00:38, 21.27it/s]
ELBO: -102946.1: 18%|#7 | 178/1000 [00:08<00:38, 21.27it/s]
ELBO: -102946.1: 18%|#7 | 179/1000 [00:08<00:41, 20.01it/s]
ELBO: -102887.3: 18%|#7 | 179/1000 [00:08<00:41, 20.01it/s]
ELBO: -102987.4: 18%|#8 | 180/1000 [00:08<00:40, 20.01it/s]
ELBO: -102954.3: 18%|#8 | 181/1000 [00:08<00:40, 20.01it/s]
ELBO: -102954.3: 18%|#8 | 182/1000 [00:08<00:37, 22.08it/s]
ELBO: -102907.4: 18%|#8 | 182/1000 [00:08<00:37, 22.08it/s]
ELBO: -102874.3: 18%|#8 | 183/1000 [00:08<00:36, 22.08it/s]
ELBO: -102953.0: 18%|#8 | 184/1000 [00:08<00:36, 22.08it/s]
ELBO: -102953.0: 18%|#8 | 185/1000 [00:08<00:40, 20.31it/s]
ELBO: -102838.3: 18%|#8 | 185/1000 [00:08<00:40, 20.31it/s]
ELBO: -102913.1: 19%|#8 | 186/1000 [00:08<00:40, 20.31it/s]
ELBO: -102830.6: 19%|#8 | 187/1000 [00:08<00:40, 20.31it/s]
ELBO: -102830.6: 19%|#8 | 188/1000 [00:08<00:40, 20.29it/s]
ELBO: -102821.6: 19%|#8 | 188/1000 [00:08<00:40, 20.29it/s]
ELBO: -102967.6: 19%|#8 | 189/1000 [00:08<00:39, 20.29it/s]
ELBO: -102879.2: 19%|#9 | 190/1000 [00:08<00:39, 20.29it/s]
ELBO: -102879.2: 19%|#9 | 191/1000 [00:08<00:39, 20.59it/s]
ELBO: -102780.0: 19%|#9 | 191/1000 [00:09<00:39, 20.59it/s]
ELBO: -102854.0: 19%|#9 | 192/1000 [00:09<00:39, 20.59it/s]
ELBO: -102864.2: 19%|#9 | 193/1000 [00:09<00:39, 20.59it/s]
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ELBO: -99538.9: : 1052it [00:57, 16.76it/s]
ELBO: -99555.7: : 1052it [00:57, 16.76it/s]
ELBO: -99563.7: : 1053it [00:57, 16.76it/s]
ELBO: -99480.5: : 1054it [00:57, 16.76it/s]
ELBO: -99480.5: : 1055it [00:57, 19.29it/s]
ELBO: -99535.4: : 1055it [00:57, 19.29it/s]
ELBO: -99539.9: : 1056it [00:57, 19.29it/s]
ELBO: -99568.1: : 1057it [00:57, 19.29it/s]
ELBO: -99568.1: : 1058it [00:57, 15.92it/s]
ELBO: -99462.3: : 1058it [00:58, 15.92it/s]
ELBO: -99498.9: : 1059it [00:58, 15.92it/s]
ELBO: -99529.6: : 1060it [00:58, 15.92it/s]
ELBO: -99529.6: : 1061it [00:58, 17.64it/s]
ELBO: -99555.3: : 1061it [00:58, 17.64it/s]
ELBO: -99524.8: : 1062it [00:58, 17.64it/s]
ELBO: -99522.9: : 1063it [00:58, 17.64it/s]
ELBO: -99522.9: : 1064it [00:58, 16.39it/s]
ELBO: -99510.0: : 1064it [00:58, 16.39it/s]
ELBO: -99497.7: : 1065it [00:58, 16.39it/s]
ELBO: -99497.7: : 1066it [00:58, 16.32it/s]
ELBO: -99529.7: : 1066it [00:58, 16.32it/s]
ELBO: -99532.9: : 1067it [00:58, 16.32it/s]
ELBO: -99532.9: : 1068it [00:58, 16.33it/s]
ELBO: -99532.9: 100%|##########| 1000/1000 [00:58<00:00, 17.08it/s]
Fitting SLDS with Laplace-EM
0%| | 0/150 [00:00<?, ?it/s]
ELBO: -120670.0: 0%| | 0/150 [00:00<?, ?it/s]
ELBO: -96943.6: 0%| | 0/150 [00:00<?, ?it/s]
ELBO: -96943.6: 1%| | 1/150 [00:00<01:26, 1.72it/s]
ELBO: -96841.8: 1%| | 1/150 [00:00<01:26, 1.72it/s]
ELBO: -96841.8: 1%|1 | 2/150 [00:00<00:57, 2.57it/s]
ELBO: -96709.4: 1%|1 | 2/150 [00:01<00:57, 2.57it/s]
ELBO: -96709.4: 2%|2 | 3/150 [00:01<01:04, 2.29it/s]
ELBO: -96770.5: 2%|2 | 3/150 [00:01<01:04, 2.29it/s]
ELBO: -96770.5: 3%|2 | 4/150 [00:01<01:00, 2.41it/s]
ELBO: -96783.8: 3%|2 | 4/150 [00:02<01:00, 2.41it/s]
ELBO: -96783.8: 3%|3 | 5/150 [00:02<01:01, 2.37it/s]
ELBO: -96735.2: 3%|3 | 5/150 [00:02<01:01, 2.37it/s]
ELBO: -96735.2: 4%|4 | 6/150 [00:02<01:06, 2.18it/s]
ELBO: -96755.2: 4%|4 | 6/150 [00:03<01:06, 2.18it/s]
ELBO: -96755.2: 5%|4 | 7/150 [00:03<01:13, 1.96it/s]
ELBO: -96723.8: 5%|4 | 7/150 [00:03<01:13, 1.96it/s]
ELBO: -96723.8: 5%|5 | 8/150 [00:03<01:10, 2.01it/s]
ELBO: -96797.0: 5%|5 | 8/150 [00:04<01:10, 2.01it/s]
ELBO: -96797.0: 6%|6 | 9/150 [00:04<01:09, 2.04it/s]
ELBO: -96759.4: 6%|6 | 9/150 [00:04<01:09, 2.04it/s]
ELBO: -96759.4: 7%|6 | 10/150 [00:04<01:03, 2.19it/s]
ELBO: -96756.2: 7%|6 | 10/150 [00:05<01:03, 2.19it/s]
ELBO: -96756.2: 7%|7 | 11/150 [00:05<01:04, 2.15it/s]
ELBO: -96703.0: 7%|7 | 11/150 [00:05<01:04, 2.15it/s]
ELBO: -96703.0: 8%|8 | 12/150 [00:05<01:00, 2.28it/s]
ELBO: -96720.8: 8%|8 | 12/150 [00:05<01:00, 2.28it/s]
ELBO: -96720.8: 9%|8 | 13/150 [00:05<00:52, 2.62it/s]
ELBO: -96711.5: 9%|8 | 13/150 [00:06<00:52, 2.62it/s]
ELBO: -96711.5: 9%|9 | 14/150 [00:06<00:51, 2.62it/s]
ELBO: -96751.7: 9%|9 | 14/150 [00:06<00:51, 2.62it/s]
ELBO: -96751.7: 10%|# | 15/150 [00:06<00:56, 2.38it/s]
ELBO: -96692.2: 10%|# | 15/150 [00:06<00:56, 2.38it/s]
ELBO: -96692.2: 11%|# | 16/150 [00:06<00:47, 2.82it/s]
ELBO: -96702.2: 11%|# | 16/150 [00:07<00:47, 2.82it/s]
ELBO: -96702.2: 11%|#1 | 17/150 [00:07<00:45, 2.93it/s]
ELBO: -96713.2: 11%|#1 | 17/150 [00:07<00:45, 2.93it/s]
ELBO: -96713.2: 12%|#2 | 18/150 [00:07<00:51, 2.55it/s]
ELBO: -96718.1: 12%|#2 | 18/150 [00:08<00:51, 2.55it/s]
ELBO: -96718.1: 13%|#2 | 19/150 [00:08<00:54, 2.42it/s]
ELBO: -96727.8: 13%|#2 | 19/150 [00:08<00:54, 2.42it/s]
ELBO: -96727.8: 13%|#3 | 20/150 [00:08<00:46, 2.80it/s]
ELBO: -96720.3: 13%|#3 | 20/150 [00:08<00:46, 2.80it/s]
ELBO: -96720.3: 14%|#4 | 21/150 [00:08<00:44, 2.90it/s]
ELBO: -96772.4: 14%|#4 | 21/150 [00:09<00:44, 2.90it/s]
ELBO: -96772.4: 15%|#4 | 22/150 [00:09<00:48, 2.63it/s]
ELBO: -96685.7: 15%|#4 | 22/150 [00:09<00:48, 2.63it/s]
ELBO: -96685.7: 15%|#5 | 23/150 [00:09<00:49, 2.56it/s]
ELBO: -96718.1: 15%|#5 | 23/150 [00:10<00:49, 2.56it/s]
ELBO: -96718.1: 16%|#6 | 24/150 [00:10<00:54, 2.31it/s]
ELBO: -96692.9: 16%|#6 | 24/150 [00:10<00:54, 2.31it/s]
ELBO: -96692.9: 17%|#6 | 25/150 [00:10<00:52, 2.38it/s]
ELBO: -96745.6: 17%|#6 | 25/150 [00:10<00:52, 2.38it/s]
ELBO: -96745.6: 17%|#7 | 26/150 [00:10<00:54, 2.26it/s]
ELBO: -96691.6: 17%|#7 | 26/150 [00:11<00:54, 2.26it/s]
ELBO: -96691.6: 18%|#8 | 27/150 [00:11<00:55, 2.22it/s]
ELBO: -96708.1: 18%|#8 | 27/150 [00:11<00:55, 2.22it/s]
ELBO: -96708.1: 19%|#8 | 28/150 [00:11<00:50, 2.42it/s]
ELBO: -96707.5: 19%|#8 | 28/150 [00:12<00:50, 2.42it/s]
ELBO: -96707.5: 19%|#9 | 29/150 [00:12<00:48, 2.49it/s]
ELBO: -96706.6: 19%|#9 | 29/150 [00:12<00:48, 2.49it/s]
ELBO: -96706.6: 20%|## | 30/150 [00:12<00:43, 2.73it/s]
ELBO: -96740.7: 20%|## | 30/150 [00:12<00:43, 2.73it/s]
ELBO: -96740.7: 21%|## | 31/150 [00:12<00:47, 2.53it/s]
ELBO: -96762.0: 21%|## | 31/150 [00:13<00:47, 2.53it/s]
ELBO: -96762.0: 21%|##1 | 32/150 [00:13<00:42, 2.81it/s]
ELBO: -96706.7: 21%|##1 | 32/150 [00:13<00:42, 2.81it/s]
ELBO: -96706.7: 22%|##2 | 33/150 [00:13<00:46, 2.54it/s]
ELBO: -96646.4: 22%|##2 | 33/150 [00:13<00:46, 2.54it/s]
ELBO: -96646.4: 23%|##2 | 34/150 [00:13<00:41, 2.79it/s]
ELBO: -96680.7: 23%|##2 | 34/150 [00:14<00:41, 2.79it/s]
ELBO: -96680.7: 23%|##3 | 35/150 [00:14<00:46, 2.50it/s]
ELBO: -96698.9: 23%|##3 | 35/150 [00:14<00:46, 2.50it/s]
ELBO: -96698.9: 24%|##4 | 36/150 [00:14<00:48, 2.33it/s]
ELBO: -96716.7: 24%|##4 | 36/150 [00:15<00:48, 2.33it/s]
ELBO: -96716.7: 25%|##4 | 37/150 [00:15<00:51, 2.21it/s]
ELBO: -96728.0: 25%|##4 | 37/150 [00:15<00:51, 2.21it/s]
ELBO: -96728.0: 25%|##5 | 38/150 [00:15<00:53, 2.10it/s]
ELBO: -96695.5: 25%|##5 | 38/150 [00:16<00:53, 2.10it/s]
ELBO: -96695.5: 26%|##6 | 39/150 [00:16<00:54, 2.05it/s]
ELBO: -96665.7: 26%|##6 | 39/150 [00:16<00:54, 2.05it/s]
ELBO: -96665.7: 27%|##6 | 40/150 [00:16<00:47, 2.31it/s]
ELBO: -96664.7: 27%|##6 | 40/150 [00:17<00:47, 2.31it/s]
ELBO: -96664.7: 27%|##7 | 41/150 [00:17<00:49, 2.18it/s]
ELBO: -96663.2: 27%|##7 | 41/150 [00:17<00:49, 2.18it/s]
ELBO: -96663.2: 28%|##8 | 42/150 [00:17<00:43, 2.49it/s]
ELBO: -96673.5: 28%|##8 | 42/150 [00:17<00:43, 2.49it/s]
ELBO: -96673.5: 29%|##8 | 43/150 [00:17<00:40, 2.63it/s]
ELBO: -96708.3: 29%|##8 | 43/150 [00:18<00:40, 2.63it/s]
ELBO: -96708.3: 29%|##9 | 44/150 [00:18<00:41, 2.55it/s]
ELBO: -96727.4: 29%|##9 | 44/150 [00:18<00:41, 2.55it/s]
ELBO: -96727.4: 30%|### | 45/150 [00:18<00:42, 2.47it/s]
ELBO: -96644.7: 30%|### | 45/150 [00:18<00:42, 2.47it/s]
ELBO: -96644.7: 31%|### | 46/150 [00:18<00:37, 2.75it/s]
ELBO: -96672.0: 31%|### | 46/150 [00:19<00:37, 2.75it/s]
ELBO: -96672.0: 31%|###1 | 47/150 [00:19<00:37, 2.71it/s]
ELBO: -96669.8: 31%|###1 | 47/150 [00:19<00:37, 2.71it/s]
ELBO: -96669.8: 32%|###2 | 48/150 [00:19<00:39, 2.59it/s]
ELBO: -96667.0: 32%|###2 | 48/150 [00:20<00:39, 2.59it/s]
ELBO: -96667.0: 33%|###2 | 49/150 [00:20<00:36, 2.80it/s]
ELBO: -96659.0: 33%|###2 | 49/150 [00:20<00:36, 2.80it/s]
ELBO: -96659.0: 33%|###3 | 50/150 [00:20<00:37, 2.67it/s]
ELBO: -96712.8: 33%|###3 | 50/150 [00:20<00:37, 2.67it/s]
ELBO: -96712.8: 34%|###4 | 51/150 [00:20<00:37, 2.63it/s]
ELBO: -96687.6: 34%|###4 | 51/150 [00:21<00:37, 2.63it/s]
ELBO: -96687.6: 35%|###4 | 52/150 [00:21<00:38, 2.52it/s]
ELBO: -96622.8: 35%|###4 | 52/150 [00:21<00:38, 2.52it/s]
ELBO: -96622.8: 35%|###5 | 53/150 [00:21<00:40, 2.42it/s]
ELBO: -96623.8: 35%|###5 | 53/150 [00:22<00:40, 2.42it/s]
ELBO: -96623.8: 36%|###6 | 54/150 [00:22<00:42, 2.27it/s]
ELBO: -96647.4: 36%|###6 | 54/150 [00:22<00:42, 2.27it/s]
ELBO: -96647.4: 37%|###6 | 55/150 [00:22<00:40, 2.32it/s]
ELBO: -96663.5: 37%|###6 | 55/150 [00:23<00:40, 2.32it/s]
ELBO: -96663.5: 37%|###7 | 56/150 [00:23<00:37, 2.50it/s]
ELBO: -96700.3: 37%|###7 | 56/150 [00:23<00:37, 2.50it/s]
ELBO: -96700.3: 38%|###8 | 57/150 [00:23<00:36, 2.57it/s]
ELBO: -96674.9: 38%|###8 | 57/150 [00:23<00:36, 2.57it/s]
ELBO: -96674.9: 39%|###8 | 58/150 [00:23<00:32, 2.84it/s]
ELBO: -96693.0: 39%|###8 | 58/150 [00:24<00:32, 2.84it/s]
ELBO: -96693.0: 39%|###9 | 59/150 [00:24<00:32, 2.78it/s]
ELBO: -96682.4: 39%|###9 | 59/150 [00:24<00:32, 2.78it/s]
ELBO: -96682.4: 40%|#### | 60/150 [00:24<00:36, 2.45it/s]
ELBO: -96676.6: 40%|#### | 60/150 [00:25<00:36, 2.45it/s]
ELBO: -96676.6: 41%|#### | 61/150 [00:25<00:37, 2.35it/s]
ELBO: -96627.5: 41%|#### | 61/150 [00:25<00:37, 2.35it/s]
ELBO: -96627.5: 41%|####1 | 62/150 [00:25<00:41, 2.13it/s]
ELBO: -96705.7: 41%|####1 | 62/150 [00:26<00:41, 2.13it/s]
ELBO: -96705.7: 42%|####2 | 63/150 [00:26<00:40, 2.13it/s]
ELBO: -96684.4: 42%|####2 | 63/150 [00:26<00:40, 2.13it/s]
ELBO: -96684.4: 43%|####2 | 64/150 [00:26<00:40, 2.14it/s]
ELBO: -96640.2: 43%|####2 | 64/150 [00:26<00:40, 2.14it/s]
ELBO: -96640.2: 43%|####3 | 65/150 [00:26<00:37, 2.24it/s]
ELBO: -96666.7: 43%|####3 | 65/150 [00:27<00:37, 2.24it/s]
ELBO: -96666.7: 44%|####4 | 66/150 [00:27<00:36, 2.33it/s]
ELBO: -96689.3: 44%|####4 | 66/150 [00:27<00:36, 2.33it/s]
ELBO: -96689.3: 45%|####4 | 67/150 [00:27<00:34, 2.40it/s]
ELBO: -96739.8: 45%|####4 | 67/150 [00:28<00:34, 2.40it/s]
ELBO: -96739.8: 45%|####5 | 68/150 [00:28<00:39, 2.06it/s]
ELBO: -96663.0: 45%|####5 | 68/150 [00:28<00:39, 2.06it/s]
ELBO: -96663.0: 46%|####6 | 69/150 [00:28<00:41, 1.95it/s]
ELBO: -96599.4: 46%|####6 | 69/150 [00:29<00:41, 1.95it/s]
ELBO: -96599.4: 47%|####6 | 70/150 [00:29<00:39, 2.03it/s]
ELBO: -96684.6: 47%|####6 | 70/150 [00:29<00:39, 2.03it/s]
ELBO: -96684.6: 47%|####7 | 71/150 [00:29<00:35, 2.24it/s]
ELBO: -96679.3: 47%|####7 | 71/150 [00:30<00:35, 2.24it/s]
ELBO: -96679.3: 48%|####8 | 72/150 [00:30<00:32, 2.42it/s]
ELBO: -96645.9: 48%|####8 | 72/150 [00:30<00:32, 2.42it/s]
ELBO: -96645.9: 49%|####8 | 73/150 [00:30<00:32, 2.37it/s]
ELBO: -96705.7: 49%|####8 | 73/150 [00:31<00:32, 2.37it/s]
ELBO: -96705.7: 49%|####9 | 74/150 [00:31<00:36, 2.10it/s]
ELBO: -96645.4: 49%|####9 | 74/150 [00:31<00:36, 2.10it/s]
ELBO: -96645.4: 50%|##### | 75/150 [00:31<00:36, 2.04it/s]
ELBO: -96712.4: 50%|##### | 75/150 [00:32<00:36, 2.04it/s]
ELBO: -96712.4: 51%|##### | 76/150 [00:32<00:35, 2.11it/s]
ELBO: -96643.9: 51%|##### | 76/150 [00:32<00:35, 2.11it/s]
ELBO: -96643.9: 51%|#####1 | 77/150 [00:32<00:31, 2.33it/s]
ELBO: -96678.2: 51%|#####1 | 77/150 [00:32<00:31, 2.33it/s]
ELBO: -96678.2: 52%|#####2 | 78/150 [00:32<00:28, 2.50it/s]
ELBO: -96671.4: 52%|#####2 | 78/150 [00:33<00:28, 2.50it/s]
ELBO: -96671.4: 53%|#####2 | 79/150 [00:33<00:27, 2.56it/s]
ELBO: -96692.3: 53%|#####2 | 79/150 [00:33<00:27, 2.56it/s]
ELBO: -96692.3: 53%|#####3 | 80/150 [00:33<00:30, 2.32it/s]
ELBO: -96638.9: 53%|#####3 | 80/150 [00:34<00:30, 2.32it/s]
ELBO: -96638.9: 54%|#####4 | 81/150 [00:34<00:30, 2.24it/s]
ELBO: -96689.4: 54%|#####4 | 81/150 [00:34<00:30, 2.24it/s]
ELBO: -96689.4: 55%|#####4 | 82/150 [00:34<00:26, 2.55it/s]
ELBO: -96664.6: 55%|#####4 | 82/150 [00:34<00:26, 2.55it/s]
ELBO: -96664.6: 55%|#####5 | 83/150 [00:34<00:24, 2.70it/s]
ELBO: -96644.0: 55%|#####5 | 83/150 [00:34<00:24, 2.70it/s]
ELBO: -96644.0: 56%|#####6 | 84/150 [00:34<00:23, 2.79it/s]
ELBO: -96666.4: 56%|#####6 | 84/150 [00:35<00:23, 2.79it/s]
ELBO: -96666.4: 57%|#####6 | 85/150 [00:35<00:26, 2.49it/s]
ELBO: -96689.5: 57%|#####6 | 85/150 [00:35<00:26, 2.49it/s]
ELBO: -96689.5: 57%|#####7 | 86/150 [00:35<00:26, 2.38it/s]
ELBO: -96635.0: 57%|#####7 | 86/150 [00:36<00:26, 2.38it/s]
ELBO: -96635.0: 58%|#####8 | 87/150 [00:36<00:24, 2.57it/s]
ELBO: -96673.4: 58%|#####8 | 87/150 [00:36<00:24, 2.57it/s]
ELBO: -96673.4: 59%|#####8 | 88/150 [00:36<00:22, 2.70it/s]
ELBO: -96629.3: 59%|#####8 | 88/150 [00:37<00:22, 2.70it/s]
ELBO: -96629.3: 59%|#####9 | 89/150 [00:37<00:23, 2.56it/s]
ELBO: -96646.1: 59%|#####9 | 89/150 [00:37<00:23, 2.56it/s]
ELBO: -96646.1: 60%|###### | 90/150 [00:37<00:21, 2.79it/s]
ELBO: -96600.3: 60%|###### | 90/150 [00:37<00:21, 2.79it/s]
ELBO: -96600.3: 61%|###### | 91/150 [00:37<00:21, 2.68it/s]
ELBO: -96624.6: 61%|###### | 91/150 [00:38<00:21, 2.68it/s]
ELBO: -96624.6: 61%|######1 | 92/150 [00:38<00:21, 2.64it/s]
ELBO: -96661.5: 61%|######1 | 92/150 [00:38<00:21, 2.64it/s]
ELBO: -96661.5: 62%|######2 | 93/150 [00:38<00:20, 2.74it/s]
ELBO: -96715.8: 62%|######2 | 93/150 [00:38<00:20, 2.74it/s]
ELBO: -96715.8: 63%|######2 | 94/150 [00:38<00:20, 2.68it/s]
ELBO: -96680.5: 63%|######2 | 94/150 [00:39<00:20, 2.68it/s]
ELBO: -96680.5: 63%|######3 | 95/150 [00:39<00:20, 2.67it/s]
ELBO: -96639.7: 63%|######3 | 95/150 [00:39<00:20, 2.67it/s]
ELBO: -96639.7: 64%|######4 | 96/150 [00:39<00:22, 2.42it/s]
ELBO: -96644.2: 64%|######4 | 96/150 [00:40<00:22, 2.42it/s]
ELBO: -96644.2: 65%|######4 | 97/150 [00:40<00:21, 2.48it/s]
ELBO: -96666.4: 65%|######4 | 97/150 [00:40<00:21, 2.48it/s]
ELBO: -96666.4: 65%|######5 | 98/150 [00:40<00:22, 2.33it/s]
ELBO: -96678.8: 65%|######5 | 98/150 [00:41<00:22, 2.33it/s]
ELBO: -96678.8: 66%|######6 | 99/150 [00:41<00:25, 2.03it/s]
ELBO: -96625.2: 66%|######6 | 99/150 [00:41<00:25, 2.03it/s]
ELBO: -96625.2: 67%|######6 | 100/150 [00:41<00:22, 2.24it/s]
ELBO: -96627.3: 67%|######6 | 100/150 [00:41<00:22, 2.24it/s]
ELBO: -96627.3: 67%|######7 | 101/150 [00:41<00:21, 2.33it/s]
ELBO: -96647.3: 67%|######7 | 101/150 [00:42<00:21, 2.33it/s]
ELBO: -96647.3: 68%|######8 | 102/150 [00:42<00:26, 1.80it/s]
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<matplotlib.colorbar.Colorbar object at 0x1724f3ee0>
# +
import autograd.numpy as np
import autograd.numpy.random as npr
npr.seed(0)
import matplotlib.pyplot as plt
# %matplotlib inline
import seaborn as sns
sns.set_style("white")
sns.set_context("talk")
import ssm
from ssm.util import random_rotation, find_permutation
# -
# Set the parameters of the SLDS
T = 1000 # number of time bins
K = 5 # number of discrete states
D = 2 # number of latent dimensions
N = 100 # number of observed dimensions
# +
# Make an SLDS with the true parameters
true_slds = ssm.SLDS(N, K, D, emissions="poisson_orthog", emission_kwargs=dict(link="softplus"))
# Set rotational dynamics
for k in range(K):
true_slds.dynamics.As[k] = .95 * random_rotation(D, theta=(k+1) * np.pi/20)
true_slds.dynamics.bs[k] = 3 * npr.randn(D)
# Set an offset to make the counts larger
# true_slds.emissions.ds += 10
# Sample data
z, x, y = true_slds.sample(T)
# Mask off some data
mask = npr.rand(T, N) < 0.95
y_masked = y * mask
# -
plt.imshow(y.T, aspect="auto", interpolation="none")
plt.xlabel("time")
plt.ylabel("neuron")
plt.colorbar()
# +
print("Fitting SLDS with BBVI")
slds = ssm.SLDS(N, K, D, emissions="poisson_orthog", emission_kwargs=dict(link="softplus"))
slds.initialize(y_masked, masks=mask)
q_bbvi_elbos, q_bbvi = slds.fit(y_masked, masks=mask, method="bbvi",
variational_posterior="tridiag",
initial_variance=1,
num_iters=1000, print_intvl=100, initialize=False)
q_bbvi_x = q_bbvi.mean[0]
# Find the permutation that matches the true and inferred states
slds.permute(find_permutation(z, slds.most_likely_states(q_bbvi_x, y)))
q_bbvi_z = slds.most_likely_states(q_bbvi_x, y)
# Smooth the observations
q_bbvi_y = slds.smooth(q_bbvi_x, y)
# +
print("Fitting SLDS with Laplace-EM")
slds = ssm.SLDS(N, K, D, emissions="poisson_orthog", emission_kwargs=dict(link="softplus"))
slds.initialize(y_masked, masks=mask)
q_lem_elbos, q_lem = slds.fit(y_masked, masks=mask, method="laplace_em",
variational_posterior="structured_meanfield",
num_iters=150, initialize=False, alpha=0)
q_lem_x = q_lem.mean_continuous_states[0]
# Find the permutation that matches the true and inferred states
slds.permute(find_permutation(z, slds.most_likely_states(q_lem_x, y)))
q_lem_z = slds.most_likely_states(q_lem_x, y)
# Smooth the data under the variational posterior
q_lem_y = slds.smooth(q_lem_x, y)
# -
plt.plot(q_bbvi_elbos, label="BBVI")
plt.plot(q_lem_elbos[1:], label="Laplace-EM")
plt.xlabel("Iteration")
plt.ylabel("ELBO")
plt.legend()
plt.plot(q_lem_elbos[1:], label="Laplace-EM")
plt.xlabel("Iteration")
plt.ylabel("ELBO")
plt.legend()
# +
# Plot the true and inferred states
xlim = (0, 1000)
plt.figure(figsize=(8,4))
plt.imshow(np.column_stack((z, q_lem_z, q_bbvi_z)).T, aspect="auto")
plt.plot(xlim, [0.5, 0.5], '-k', lw=2)
plt.yticks([0, 1, 2], ["$z_{\\mathrm{true}}$", "$z_{\\mathrm{LEM}}$", "$z_{\\mathrm{BBVI}}$"])
plt.xlim(xlim)
# -
plt.figure(figsize=(8,4))
plt.plot(x, '-k')
plt.plot(q_bbvi_x, '-')
plt.ylabel("$x$")
plt.xlim(xlim)
# +
# Plot the smoothed observations
lim = max(y.max(), q_bbvi_y.max(), q_lem_y.max())
plt.figure(figsize=(18,6))
plt.subplot(131)
plt.imshow(y.T, aspect="auto", vmin=0, vmax=lim)
plt.ylabel("neuron")
plt.xlabel("time")
plt.title("Data")
plt.colorbar()
plt.subplot(132)
plt.imshow(q_lem_y.T, aspect="auto", vmin=0, vmax=lim)
plt.xlabel("time")
plt.title("Inferred Rate, Laplace-EM")
plt.colorbar()
plt.subplot(133)
plt.imshow(q_bbvi_y.T, aspect="auto", vmin=0, vmax=lim)
plt.xlabel("time")
plt.title("Inferred Rate, BBVI")
plt.colorbar()
Total running time of the script: ( 2 minutes 2.550 seconds)