[DL輪読会]Economy stastistical recurrent units for inferring nonlinear granger causality
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2020/01/17 Deep Learning JP: http://deeplearning.jp/seminar-2/
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DEEP LEARNING JP
[DL Papers]
http://deeplearning.jp/
ECONOMY STATISTICAL RECURRENT UNITS FOR
INFERRING NONLINEAR GRANGER CAUSALITY
Akitoshi Kimura, Taniguchi Lab, Waseda University](https://image.slidesharecdn.com/kimura20200117dlseminarv1-200117001836/85/DL-Economy-stastistical-recurrent-units-for-inferring-nonlinear-granger-causality-1-320.jpg)
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[DL輪読会]Economy stastistical recurrent units for inferring nonlinear granger causality
- 1. 1 DEEP LEARNING JP [DL Papers] http://deeplearning.jp/ ECONOMY STATISTICAL RECURRENT UNITS FOR INFERRING NONLINEAR GRANGER CAUSALITY Akitoshi Kimura, Taniguchi Lab, Waseda University
- 2. 書誌情報 • 著者: – Saurabh Khanna • Department of Electrical and Computer Engineering, National University of Singapore – Vincent Y. F. Tan • Department of Electrical and Computer Engineering, Department of Mathematics, National University of Singapore • 学会: – ICLR 2020, Accept (Poster) 2
- 3. 概要 • 非線形な相互作用を持つ確率過程における Granger 因果性 • Statistical Recurrent Unit (SRU) network のパラメータを penalized mean squared prediction error loss で推定 • (Overfitting を避けるために) Economy SRU を提案 • 各種実験で, MLP, LSTM, TCDF より良好な結果 3
- 4. 背景: Granger 因果性 • 変数 A の予測誤差が, 予測モデルに変数 B を入れると減少する とき「B から A の Granger 因果性が存在する」という – 通常 VAR モデルの OLS 残差を比較検討する (Causality test) 4
- 5. モデル • 非線形自己相関モデル – (線形) VAR モデルの拡張になっている 5
- 6. 非線形動的システムにおける Granger 因果性 • 任意の , 任意の異なる , に対し, が成り立つとき「j から I への Granger 因果性を持たない」 • をパラメータ付けされた近似関数 で置き換える – : の全パラメータ – MLP, LSTM, TCDF, SRU, eSRU 6
- 7. SRU Model 7
- 9. SRU Model におけるパラメータ推定 : の第 j 列 – もし 0 であれば,「j から I への Granger 因果性を持たない」 9
- 11. eSUR: グループスパース正則化 • Time-localized, component-specific などの, 現実世界における因 果効果の特徴を捉える 11
- 12. グループスパース正則化概念図 • 各 time scale で少数の に依存するよう制約 12
- 13. 実験 1 • Lorenz-96 model – 気候科学におけるモデリング、予測に使われる 13
- 14. 実験 2 • VAR(3) モデル 14
- 15. 実験 3 • 脳の各領域 (n=15) での血液酸素レベル依存イメージング – 脳の神経活動の因果性推定 15
- 16. 実験 4 • DREAM-3 IN SILICO NETWORK INFERENCE CHALLENGE – 遺伝子調節ネットワークの推定 16
Editor's Notes
- International Conference on Learning Representations
- MLP: multi-layer perceptron LSTM: long short-term memory TCDF: attention-gated CNN
- series j does not Granger cause series i if the component-wise generative function f_i does not depend on the past measurements in series j MLP- and LSTM-based models in Tank et al. (2018) and the attention-gated CNN-based model (referred hereafter as Temporal Causal Discovery Framework (TCDF)) in Nauta et al. (2019).
- 隠れ層に統計量の移動平均のみ保持する（gate はいらない) 統計量: データセットを表現する変数（？） いくつかの重みで移動平均を取る (DL Hacks) VAR(1) のパラメータ \alpha_1, …, \alpha_m を組み込んでいるイメージ 過去データを適当な重みで参照している…
- For values of scale \alpha ~ 1, the single-scale summary statistic u^{\alpha}_{i;t} in equation 3d is more sensitive to the recent past measurements in x. On the other hand, \alpha ~ 0 yields a summary statistic that is more representative of the older portions of the input time series.
- W_{in}^{(i)}(:, j) denotes the jth column in the weight matrix W_{in}^{(i)} W_{in}^{(i)}(:, j) being estimated as the all-zeros vector is that the past measurements in series j do not influence the predicted future value of series i. In this case, we declare that series j does not Granger-cause series i. we use first-order gradient-based methods such as stochastic gradient descent which have been found to be consistently successful in finding good solutions of nonconvex deep neural network optimization problems.
- the first and the second terms on the RHS represent the advection and the diffusion in the system, respectively, and the third term F is the magnitude of the external forcing. The system dynamics becomes increasingly chaotic for higher values of F. In the case of weak nonlinear interactions (F = 10), In case of strong nonlinear interactions (F = 40), AU (Area Under) ROC曲線(Receiver Operatorating Characteristic curve)
- estimate the connections in the human brain from simulated blood oxygenation level dependent (BOLD) imaging data.