shifts in streams: Real-time forecasting of co- evolving time sequences." Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. 2016.
ʹରͯ͠ҎԼ͕Γཱͭ ࣌ʹґଘ͠ͳ͍ l ࣍ͷϞʔϝϯτ·Ͱ͕ෆม l ҰൠతʹɺʮఆৗੑʯͱݺΕΔ࣌ɺͪ͜ΒΛࢦ͢ࣄ͕ଟ͍ l ࣗݾ૬͕ؔLͱͱʹࢦతʹݮਰ ఆৗੑඇఆৗੑ E 𝑦* = E 𝑦*(& , VAR 𝑦* = VAR 𝑦*(& Cov 𝑦* , 𝑦*(& = 𝛾& > 0 ଟ͘ͷ࣌ܥྻ౷ܭతϞσϧ͕ఆৗੑΛલఏͱ͍ͯ͠Δͨ Ίɺੳ͢Δ࣌ܥྻ͕ఆৗͰ͋Δͱخ͍͠ ఆৗੑΛલఏͱ͠ͳ͍ͱɺฏۉࢄ͕ҰఆͰແ͘ͳΔͨ Ίɺੳ͕ؤ݈Ͱͳ͘ͳΔ
and Christos Faloutsos. "Autoplait: Automatic mining of co-evolving time sequences." Proceedings of the 2014 ACM SIGMOD international conference on Management of data. 2014.
ਪఆ͞ΕΔ༧ଌ͕ਅͷΛଊ͍͑ͯΔ͔ΛධՁ l g(x)͕ਅͷ f(x)͕Ϟσϧͷͱͨ࣌͠ɺ,-ใྔҎԼͷܗ l D`a (g| 𝑓 = 0ͷ࣌ɺ g x = f(x) l ࡾ֯ෆࣜରশੑͳͲͷڑͷެཧຬͨ͞ͳ͍ Def (g||𝑓) = ~ +T T g x log g x f x 𝑑𝑥 ∗ Def (g||𝑓) ≥ 0
g x log g x 𝑑𝑥 − m -b b g x log 𝑓 x 𝑑𝑥 g x ~ N 𝜇c , 𝜎c Z , f x ~ N 𝜇d , 𝜎d Z m -b b g x log 𝑓 x 𝑑𝑥 = − 1 2 log2π𝜎d Z − 𝜎c Z + 𝜇c − 𝜇d Z 2𝜎d Z m -b b g x log g x 𝑑𝑥 = − 1 2 log2π𝜎c Z − 1 2 正規分布の確率密度関数
1 𝑛 ? '"* , log f x|𝜃-./ ͜ͷ෦Λ ิਖ਼͍ͨ͠ʂ ฏۉର ର ظΛͱΔ 𝔼0[𝐷] = t #$ $ g x [D]𝑑𝑥 ͜ͷิਖ਼෦͕ύϥϝʔλͰ͋Δ 𝑝ʹۙࣅͰ͖Δ ิਖ਼ 𝐷 = 1 𝑛 ? '"* , log f x|𝜃-./ − t #$ $ g x log f x|𝜃-./ 𝑑𝑥
౷ܭϞσϧͷࢦඪͱͳΔ l 𝑝ࣗ༝ύϥϝʔλ l ͜ͷࢦඪ͕খ͍͞౷ܭϞσϧ͕ྑ͍Ϟσϧͱਪఆ͞ΕΔ l ใྔج४ͷछ ∑!/% ' log f x|𝜃1gh − 𝑝= n ∫ +T T g x log f x|𝜃1gh 𝑑𝑥 AIC = −2 ) !/% ' log f x|𝜃1gh + 2𝑝
ྗΛઙ͍χϡʔϥϧωοτϫʔΫͰද ݱ͠Α͏ͱ͢Δͱେ͖ͳԣ෯ χϡʔ ϩϯ ͕ඞཁ Montufar, Guido F., et al. "On the number of linear regions of deep neural networks." Advances in neural information processing systems 27 (2014). Arora, R., Basu, A., Mianjy, P., & Mukherjee, A. (2016). Understanding deep neural networks with rectified linear units. arXiv preprint arXiv:1611.01491.
l ͜ͷ๏ଇ͕ݴޠɾը૾ɾಈըͳͲ ͷ༷ʑͳλεΫʹద༻͞ΕΔ͜ͱ Λࣔ͢ from: Henighan, Tom, Jared Kaplan, Mor Katz, Mark Chen, Christopher Hesse, Jacob Jackson, Heewoo Jun et al. "Scaling laws for autoregressive generative modeling." arXiv preprint arXiv:2010.14701 (2020).
l χϡʔϥϧωοτϫʔΫͰ൚Խޡࠩͱ܇࿅ޡࠩͷ͕ࠩখ͘͞ͳ ΔͨΊʁʢཧతੳ͕ߦΘΕ͍ͯΔʣ Neyshabur, Behnam, et al. "The role of over- parametrization in generalization of neural networks." 7th International Conference on Learning Representations, ICLR 2019. 2019.
Zen, H., Simonyan, K., Vinyals, O., Graves, A., ... & Kavukcuoglu, K. (2016). Wavenet: A generative model for raw audio. arXiv preprint arXiv:1609.03499. l $//Λ༻͍ͨ࣌ؒܗ Իੜ ʹର͢Δ֬తੜϞσϧͰ͋Δ 8BWF/FUͰఏҊ͞Εͨߏཁૉͷͭɻ l ೖྗ͔ΒॱʹͦΕͧΕɺɺɺݸͣͭεΩοϓ͠ͳ͕ΒΈࠐ ΈΛܭࢉɻΈࠐΈͷਂ͞ʹԠͯ͡ɺೖྗͰ͖Δܥྻ͕ࢦతʹ ૿Ճ͍ͯ͘͠ɻ l શ݁߹//ͷΑ͏ʹύϥϝʔλ͕ଟ͘ͳ͘ɺ3//ͷΑ͏ʹճؼతͳ ଓ͕ແ͍ͷͰɺֶश͕3//ΑΓ͘ͳ͍ͬͯΔ l ظͷܥྻΛೖྗͱͯ͠ޯফࣦ͕ੜ͡ͳ͍
from: Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A. N., ... & Polosukhin, I. (2017). Attention is all you need. Advances in neural information processing systems, 30.
& O'Banion, S. (2020). Deep transformer models for time series forecasting: The influenza prevalence case. arXiv preprint arXiv:2001.08317. .σʔληοτͷTUFQBIFBE GPSFDBTUJOHͷਫ਼ݕূ
͞Ε͓ͯΓɺղऍੑͷߴ͍Ϟσϧ ͱͳ͍ͬͯΔʢͲͷ෦ͰԠͯ͠ ͍Δ͔͕͔Δʣ from: Oreshkin, Boris N., et al. "N-BEATS: Neural basis expansion analysis for interpretable time series forecasting." International Conference on Learning Representations. 2019.
l )JQQPߦྻΛ3//ʹΈࠐΉ͜ͱͰظهԱੑΛ֫ಘ from: Gu, Albert, Karan Goel, and Christopher Re. "Efficiently Modeling Long Sequences with Structured State Spaces." International Conference on Learning Representations. 2021.
"DeepAR: Probabilistic forecasting with autoregressive recurrent networks." International Journal of Forecasting 36.3 (2020): 1181-1191. l %FFQ"3 l ֬తͳ༧ଌΛ࣮ݱ͢ΔͨΊʹෛͷೋ߲ؔͱϞϯςΧϧϩαϯϓ Ϧϯάͷग़ྗܗࣜͷಋೖ Training Prediction
Nicolas Thome. "Probabilistic time series forecasting with structured shape and temporal diversity." arXiv preprint arXiv:2010.07349 (2020). l 453*1& l ΨεͳͲͷҰൠతͳ Ͱͳ͘ɺඇఆৗͳ࣌ ܥྻʹରԠͨ࣌ؒ͠తɺ ܗঢ়త؍Ͱॊೈͳ༧ ଌ͕Մೳͳ&ODPEFS %FDPEFSϞσϧͷఏҊ
S. S., Benidis, K., Bohlke-Schneider, M., Kurle, R., Stella, L., ... & Januschowski, T. (2020). Normalizing kalman filters for multivariate time series analysis. Advances in Neural Information Processing Systems, 33, 2995-3007. l /PSNBMJ[JOH,BMNBO'JMJUFST l ઢܗΨεঢ়ଶۭؒϞσϧΛ/PSNBMJ[JOHGMPXͰิڧͯ͠ଟมྔ࣌ܥྻ ͷϞσϦϯάΛ࣮ݱ͢Δ l 3FBM/71ͷΞʔΩςΫνϟΛར༻
ordinary differential equations." Advances in neural information processing systems 31 (2018). l 0%&3// l &ODPEFS%FDPEFSϞσϧʹ͓͚Δσίʔμͷજࡏมग़ྗΛ0%&/FUʹ ஔ͖͑Δ͜ͱͰෆִؒ࣌ܥྻʹରԠ
ordinary differential equations." Advances in neural information processing systems 31 (2018). l /FVSBM0SEJOBSZ%JGGFSFOUJBM&RVBUJPO l 3FT/FUͱৗඋํఔࣜʹྨࣅʹண͠ɺৗඍํఔࣜͷղ๏Λχϡʔ ϥϧωοτͷදݱʹ༻͍Δख๏ l ͜ΕΛ༻͍Δ͜ͱͰϝϞϦޮͷߴ͍ ࣌ؒ࿈ଓͳϞσϧΛߏங͢Δ͜ͱ͕Մೳ ͱͳΔ l જࡏදݱ0%&4PMWFSʹΑͬͯܭࢉՄೳ
Haixu, et al. "Autoformer: Decomposition transformers with auto-correlation for long-term series forecasting." Advances in Neural Information Processing Systems 34 (2021): 22419-22430.
Josif, et al. "Learning time-series shapelets." Proceedings of the 20th ACM SIGKDD international conference on Knowledge discovery and data mining. 2014.
François Petitjean, and Geoffrey I. Webb. "ROCKET: exceptionally fast and accurate time series classification using random convolutional kernels." Data Mining and Knowledge Discovery 34.5 (2020): 1454-1495. 畳み込み Time Window 1.23 2.34 Time Window分の特徴を⽣成 ・・・ 特徴量を作成 最⼤: 2.34 正の割合: 0.21 学習
Dieuleveut, and Martin Jaggi. "Unsupervised scalable representation learning for multivariate time series." Advances in neural information processing systems 32 (2019).
"The web centipede: understanding how web communities influence each other through the lens of mainstream and alternative news sources." Proceedings of the 2017 internet measurement conference. 2017.
Kurashima, Takeshi, Tim Althoff, and Jure Leskovec. "Modeling interdependent and periodic real-world action sequences." Proceedings of the 2018 world wide web conference. 2018.
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