notesum.ai

Published at November 26

Disentangled Interpretable Representation for Efficient Long-term Time Series Forecasting

cs.LG

Released Date: November 26, 2024

Authors: Yuang Zhao¹, Tianyu Li¹, Jiadong Chen², Shenrong Ye¹, Fuxin Jiang³, Tieying Zhang³, Xiaofeng Gao²

Aff.: ¹SJTU Paris Elite Institute of Technology, Shanghai Jiao Tong University; ²Department of Computer Science and Engineering, Shanghai Jiao Tong University; ³ByteDance Inc.

Arxiv: http://arxiv.org/abs/2411.17257v1

		DiPE-Linear		FITS		RLinear		DLinear		Nlinear
		(Ours)		(ICLR-24)		(arXiv-23)		(AAAI-23)		(AAAI-23)
Metrics		MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE
ETTh1	96	0.369 $\pm$ 0.000	0.393 $\pm$ 0.000	0.380 $\pm$ 0.000	0.403 $\pm$ 0.000	0.376 $\pm$ 0.004	0.401 $\pm$ 0.004	0.388 $\pm$ 0.010	0.414 $\pm$ 0.012	0.384 $\pm$ 0.004	0.405 $\pm$ 0.003
	192	0.407 $\pm$ 0.000	0.415 $\pm$ 0.000	0.417 $\pm$ 0.001	0.425 $\pm$ 0.001	0.416 $\pm$ 0.002	0.426 $\pm$ 0.002	0.425 $\pm$ 0.005	0.436 $\pm$ 0.005	0.415 $\pm$ 0.003	0.424 $\pm$ 0.002
	336	0.424 $\pm$ 0.000	0.427 $\pm$ 0.000	0.436 $\pm$ 0.000	0.440 $\pm$ 0.000	0.444 $\pm$ 0.002	0.444 $\pm$ 0.002	0.469 $\pm$ 0.010	0.469 $\pm$ 0.009	0.445 $\pm$ 0.002	0.443 $\pm$ 0.002
	720	0.409 $\pm$ 0.000	0.439 $\pm$ 0.000	0.432 $\pm$ 0.000	0.456 $\pm$ 0.000	0.474 $\pm$ 0.002	0.481 $\pm$ 0.002	0.530 $\pm$ 0.021	0.533 $\pm$ 0.015	0.439 $\pm$ 0.002	0.470 $\pm$ 0.000
ETTh2	96	0.275 $\pm$ 0.001	0.336 $\pm$ 0.001	0.272 $\pm$ 0.000	0.336 $\pm$ 0.000	0.270 $\pm$ 0.001	0.335 $\pm$ 0.001	0.280 $\pm$ 0.005	0.345 $\pm$ 0.004	0.276 $\pm$ 0.002	0.338 $\pm$ 0.001
	192	0.325 $\pm$ 0.001	0.372 $\pm$ 0.000	0.331 $\pm$ 0.000	0.374 $\pm$ 0.000	0.335 $\pm$ 0.004	0.380 $\pm$ 0.002	0.358 $\pm$ 0.014	0.399 $\pm$ 0.011	0.345 $\pm$ 0.004	0.382 $\pm$ 0.002
	336	0.350 $\pm$ 0.002	0.393 $\pm$ 0.001	0.354 $\pm$ 0.000	0.395 $\pm$ 0.000	0.366 $\pm$ 0.005	0.409 $\pm$ 0.003	0.439 $\pm$ 0.017	0.457 $\pm$ 0.009	0.375 $\pm$ 0.009	0.411 $\pm$ 0.004
	720	0.375 $\pm$ 0.002	0.415 $\pm$ 0.001	0.378 $\pm$ 0.000	0.423 $\pm$ 0.000	0.414 $\pm$ 0.003	0.447 $\pm$ 0.001	0.657 $\pm$ 0.062	0.573 $\pm$ 0.026	0.408 $\pm$ 0.008	0.446 $\pm$ 0.003
ETTm1	96	0.309 $\pm$ 0.000	0.350 $\pm$ 0.000	0.309 $\pm$ 0.000	0.352 $\pm$ 0.001	0.309 $\pm$ 0.001	0.352 $\pm$ 0.001	0.312 $\pm$ 0.005	0.358 $\pm$ 0.006	0.318 $\pm$ 0.007	0.357 $\pm$ 0.005
	192	0.339 $\pm$ 0.000	0.369 $\pm$ 0.000	0.339 $\pm$ 0.001	0.369 $\pm$ 0.001	0.341 $\pm$ 0.004	0.370 $\pm$ 0.003	0.350 $\pm$ 0.006	0.386 $\pm$ 0.008	0.350 $\pm$ 0.007	0.377 $\pm$ 0.005
	336	0.367 $\pm$ 0.000	0.386 $\pm$ 0.000	0.368 $\pm$ 0.001	0.386 $\pm$ 0.001	0.369 $\pm$ 0.003	0.387 $\pm$ 0.003	0.379 $\pm$ 0.005	0.403 $\pm$ 0.006	0.378 $\pm$ 0.005	0.393 $\pm$ 0.004
	720	0.416 $\pm$ 0.000	0.413 $\pm$ 0.000	0.416 $\pm$ 0.000	0.413 $\pm$ 0.000	0.415 $\pm$ 0.001	0.411 $\pm$ 0.001	0.439 $\pm$ 0.011	0.443 $\pm$ 0.012	0.420 $\pm$ 0.003	0.415 $\pm$ 0.002
ETTm2	96	0.162 $\pm$ 0.000	0.252 $\pm$ 0.000	0.162 $\pm$ 0.000	0.253 $\pm$ 0.000	0.162 $\pm$ 0.000	0.251 $\pm$ 0.000	0.163 $\pm$ 0.001	0.255 $\pm$ 0.001	0.162 $\pm$ 0.000	0.252 $\pm$ 0.001
	192	0.216 $\pm$ 0.000	0.289 $\pm$ 0.000	0.216 $\pm$ 0.000	0.291 $\pm$ 0.000	0.216 $\pm$ 0.000	0.290 $\pm$ 0.000	0.219 $\pm$ 0.002	0.297 $\pm$ 0.001	0.216 $\pm$ 0.000	0.291 $\pm$ 0.000
	336	0.268 $\pm$ 0.000	0.324 $\pm$ 0.000	0.268 $\pm$ 0.000	0.326 $\pm$ 0.000	0.268 $\pm$ 0.001	0.326 $\pm$ 0.000	0.272 $\pm$ 0.003	0.334 $\pm$ 0.003	0.268 $\pm$ 0.000	0.326 $\pm$ 0.000
	720	0.353 $\pm$ 0.000	0.379 $\pm$ 0.000	0.349 $\pm$ 0.000	0.378 $\pm$ 0.000	0.354 $\pm$ 0.001	0.384 $\pm$ 0.000	0.367 $\pm$ 0.004	0.398 $\pm$ 0.003	0.349 $\pm$ 0.000	0.379 $\pm$ 0.000
Electricity	96	0.132 $\pm$ 0.000	0.228 $\pm$ 0.001	0.134 $\pm$ 0.000	0.231 $\pm$ 0.000	0.135 $\pm$ 0.000	0.232 $\pm$ 0.000	0.133 $\pm$ 0.000	0.229 $\pm$ 0.000	0.133 $\pm$ 0.000	0.228 $\pm$ 0.000
	192	0.148 $\pm$ 0.000	0.245 $\pm$ 0.000	0.149 $\pm$ 0.000	0.244 $\pm$ 0.000	0.150 $\pm$ 0.000	0.246 $\pm$ 0.000	0.148 $\pm$ 0.000	0.243 $\pm$ 0.000	0.148 $\pm$ 0.000	0.242 $\pm$ 0.000
	336	0.162 $\pm$ 0.000	0.261 $\pm$ 0.000	0.165 $\pm$ 0.000	0.260 $\pm$ 0.000	0.166 $\pm$ 0.000	0.262 $\pm$ 0.000	0.162 $\pm$ 0.000	0.261 $\pm$ 0.000	0.164 $\pm$ 0.000	0.258 $\pm$ 0.000
	720	0.198 $\pm$ 0.002	0.296 $\pm$ 0.001	0.204 $\pm$ 0.000	0.293 $\pm$ 0.000	0.206 $\pm$ 0.000	0.294 $\pm$ 0.000	0.196 $\pm$ 0.000	0.293 $\pm$ 0.001	0.203 $\pm$ 0.000	0.291 $\pm$ 0.000
Weather	96	0.142 $\pm$ 0.001	0.201 $\pm$ 0.001	0.142 $\pm$ 0.000	0.192 $\pm$ 0.000	0.143 $\pm$ 0.000	0.194 $\pm$ 0.000	0.142 $\pm$ 0.000	0.202 $\pm$ 0.000	0.142 $\pm$ 0.001	0.192 $\pm$ 0.001
	192	0.187 $\pm$ 0.003	0.253 $\pm$ 0.002	0.185 $\pm$ 0.000	0.234 $\pm$ 0.000	0.186 $\pm$ 0.000	0.235 $\pm$ 0.000	0.184 $\pm$ 0.001	0.249 $\pm$ 0.002	0.183 $\pm$ 0.000	0.234 $\pm$ 0.000
	336	0.234 $\pm$ 0.001	0.293 $\pm$ 0.002	0.235 $\pm$ 0.000	0.276 $\pm$ 0.000	0.236 $\pm$ 0.000	0.275 $\pm$ 0.000	0.236 $\pm$ 0.001	0.293 $\pm$ 0.001	0.234 $\pm$ 0.001	0.276 $\pm$ 0.000
	720	0.306 $\pm$ 0.004	0.348 $\pm$ 0.003	0.307 $\pm$ 0.000	0.328 $\pm$ 0.000	0.308 $\pm$ 0.000	0.327 $\pm$ 0.000	0.306 $\pm$ 0.002	0.349 $\pm$ 0.002	0.308 $\pm$ 0.000	0.330 $\pm$ 0.000
FaaS	96	0.280 $\pm$ 0.000	0.251 $\pm$ 0.000	0.309 $\pm$ 0.000	0.266 $\pm$ 0.000	0.306 $\pm$ 0.000	0.264 $\pm$ 0.000	0.303 $\pm$ 0.000	0.264 $\pm$ 0.000	0.305 $\pm$ 0.000	0.266 $\pm$ 0.000
	192	0.314 $\pm$ 0.000	0.279 $\pm$ 0.000	0.342 $\pm$ 0.000	0.293 $\pm$ 0.000	0.344 $\pm$ 0.000	0.292 $\pm$ 0.000	0.339 $\pm$ 0.000	0.294 $\pm$ 0.000	0.340 $\pm$ 0.000	0.292 $\pm$ 0.000
	336	0.351 $\pm$ 0.000	0.309 $\pm$ 0.000	0.368 $\pm$ 0.000	0.316 $\pm$ 0.000	0.375 $\pm$ 0.000	0.319 $\pm$ 0.000	0.367 $\pm$ 0.000	0.323 $\pm$ 0.000	0.364 $\pm$ 0.000	0.314 $\pm$ 0.000
	720	0.379 $\pm$ 0.000	0.332 $\pm$ 0.000	0.415 $\pm$ 0.000	0.348 $\pm$ 0.000	0.436 $\pm$ 0.000	0.350 $\pm$ 0.000	0.417 $\pm$ 0.000	0.364 $\pm$ 0.001	0.410 $\pm$ 0.000	0.344 $\pm$ 0.000
IaaS	96	0.789 $\pm$ 0.000	0.667 $\pm$ 0.000	0.799 $\pm$ 0.000	0.702 $\pm$ 0.000	0.797 $\pm$ 0.000	0.688 $\pm$ 0.000	0.795 $\pm$ 0.000	0.699 $\pm$ 0.000	0.799 $\pm$ 0.000	0.682 $\pm$ 0.000
	192	0.817 $\pm$ 0.000	0.698 $\pm$ 0.000	0.839 $\pm$ 0.000	0.723 $\pm$ 0.000	0.831 $\pm$ 0.000	0.700 $\pm$ 0.000	0.823 $\pm$ 0.000	0.717 $\pm$ 0.000	0.820 $\pm$ 0.000	0.702 $\pm$ 0.000
	336	1.180 $\pm$ 0.015	0.839 $\pm$ 0.010	0.998 $\pm$ 0.007	0.855 $\pm$ 0.005	1.255 $\pm$ 0.012	0.822 $\pm$ 0.007	0.842 $\pm$ 0.000	0.731 $\pm$ 0.000	0.898 $\pm$ 0.000	0.771 $\pm$ 0.000
	720	0.869 $\pm$ 0.000	0.736 $\pm$ 0.000	0.899 $\pm$ 0.000	0.839 $\pm$ 0.000	0.938 $\pm$ 0.000	0.828 $\pm$ 0.000	0.881 $\pm$ 0.000	0.741 $\pm$ 0.000	0.924 $\pm$ 0.000	0.785 $\pm$ 0.000
Illness	24	2.260 $\pm$ 0.000	0.951 $\pm$ 0.000	2.289 $\pm$ 0.000	0.975 $\pm$ 0.000	2.258 $\pm$ 0.000	0.930 $\pm$ 0.000	2.467 $\pm$ 0.000	1.079 $\pm$ 0.000	2.288 $\pm$ 0.000	0.962 $\pm$ 0.000
	36	2.162 $\pm$ 0.000	0.940 $\pm$ 0.000	2.292 $\pm$ 0.000	0.986 $\pm$ 0.000	2.213 $\pm$ 0.000	0.943 $\pm$ 0.000	2.510 $\pm$ 0.000	1.089 $\pm$ 0.000	2.221 $\pm$ 0.000	0.964 $\pm$ 0.000
	48	2.184 $\pm$ 0.000	0.956 $\pm$ 0.000	2.266 $\pm$ 0.000	0.992 $\pm$ 0.000	2.309 $\pm$ 0.000	0.979 $\pm$ 0.000	2.510 $\pm$ 0.000	1.092 $\pm$ 0.000	2.177 $\pm$ 0.000	0.970 $\pm$ 0.000
	60	2.053 $\pm$ 0.000	0.957 $\pm$ 0.000	2.221 $\pm$ 0.000	0.996 $\pm$ 0.000	2.183 $\pm$ 0.000	0.952 $\pm$ 0.000	2.599 $\pm$ 0.000	1.121 $\pm$ 0.000	2.216 $\pm$ 0.000	0.985 $\pm$ 0.000
M5	24	0.490 $\pm$ 0.000	0.497 $\pm$ 0.000	0.499 $\pm$ 0.000	0.502 $\pm$ 0.000	0.500 $\pm$ 0.000	0.503 $\pm$ 0.000	0.503 $\pm$ 0.000	0.505 $\pm$ 0.000	0.498 $\pm$ 0.000	0.502 $\pm$ 0.000
	36	0.515 $\pm$ 0.000	0.511 $\pm$ 0.000	0.523 $\pm$ 0.000	0.529 $\pm$ 0.000	0.524 $\pm$ 0.000	0.517 $\pm$ 0.000	0.533 $\pm$ 0.000	0.521 $\pm$ 0.000	0.522 $\pm$ 0.000	0.515 $\pm$ 0.000
	48	0.542 $\pm$ 0.000	0.525 $\pm$ 0.000	0.550 $\pm$ 0.000	0.530 $\pm$ 0.000	0.552 $\pm$ 0.000	0.531 $\pm$ 0.000	0.563 $\pm$ 0.000	0.537 $\pm$ 0.000	0.549 $\pm$ 0.000	0.529 $\pm$ 0.000
	60	0.565 $\pm$ 0.000	0.538 $\pm$ 0.000	0.572 $\pm$ 0.000	0.542 $\pm$ 0.000	0.575 $\pm$ 0.000	0.543 $\pm$ 0.000	0.581 $\pm$ 0.000	0.547 $\pm$ 0.000	0.570 $\pm$ 0.000	0.541 $\pm$ 0.000
Best count		32	26	7	5	7	7	6	1	9	6