MCMC: Marov Chain Monte Carlo [20] 2. VAE-NMF DNN DNN F T X x t R F t = 1,..., T x t 2. 1 Generative Adversarial Networ: GAN [21,22] GAN z t R D x t z

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1 一般社団法人電子情報通信学会 THE INSTITUTE OF ELECTRONICS, INFORMATION AND COMMUNICATION ENGINEERS THE INSTITUTE OF ELECTRONICS, INFORMATION AND COMMUNICATION ENGINEERS 信学技報 IEICE Technical Report SP TECHNICAL REPORT OF IEICE., {yoshiai, mimura, itoyama, yoshii, DNN DNN MCMC 1. [1 8] Deep Neural Networ: DNN [1,2] DAE Denoising AutoEncoder [2] DNN. DNN [3 5,9 12] Wiener filter [9] Non-negative Matrix Factorization: NMF [4,12 14] NMF [4, 13] NMF NMF Robust NMF: RNMF [15 17] RNMF NMF RNMF NMF DNN Variational AutoEncoder: VAE [18, 19] VAE DNN VAE, NMF VAE NMF VAE-NMF VAE-NMF This article is a technical report without peer review, and its polished and/or extended version may be published elsewhere. Copyright 2017 by IEICE

2 MCMC: Marov Chain Monte Carlo [20] 2. VAE-NMF DNN DNN F T X x t R F t = 1,..., T x t 2. 1 Generative Adversarial Networ: GAN [21,22] GAN z t R D x t z t f : R D R F z t N 0, 1 1 x t = f z t 2 N µ, σ µ σ f DNN Generator z t f x t z t Generator Discriminator DNN Discriminator Generator GAN Discriminator Generator GAN Generator Discriminator [23] GAN f 2. 2 VAE [18, 19] VAE z t R D VAE GAN f x t p x t z t z t N 0, 1 3 x t p x t z t 4 DNN Kingma [18] µ x f zt : RD R VAE x ft N µ x f zt, 1 5 VAE x t VAE p x t z t argmax p X = argmax px t z t px t z t p x t z t p z t dz t 6 VAE [20] z t q z t : p z 1,..., z t X q z t = q z dt 7 t = N µ z d xt, σz d xt 8 µ z d : RF R σ z d : RF R + DNN log p X log p X = log p x t z t p z t dz t 9 q z t log = KL [q z t p z t ] + p xt zt p zt dz t 10 q z t E q [log p x t z t ] 11 KL [ ] Kullbac-Leibler VAE q z t p x t z t DNN 11 Stochastic Gradient Descent: SGD 3. VAE NMF VAE NMF VAE-NMF 3. 1 : X C F T : S C F T F T Short Time Fourier Transform: STFT - 2-2

.., w K] R F K + H R K T + n ft N C 0, w f h t 15 W H w f G a 0, b 0 16 h t G a 0, b 0 17 tt G a, b a b a 0 b 0 W H S N x ft N C 0, σ s f zt + w f h t 18 X x ft 2 Exp σ s f zt + w f h t 19 x ft 2 x

3 ss fftt σσ ff ss zz tt 1: VAE 3. 2 VAE zz zz ddtt VAE D Z R D T z t F0 z t VAE VAE Z z dt N 0, 1 12 Z Power Spectral Density: PSD S Z 0 1. s ft N C 0, σ s f zt 13 N C µ, σ µ σ σ s f zt : RD R + Z S DNN VAE 3. 3 VAE VAE-NMF X S N C F T x ft = s ft + n ft 14 S VAE PSD NMF K W = [w 1,..., w K] R F K + H R K T + n ft N C 0, w f h t 15 W H w f G a 0, b 0 16 h t G a 0, b 0 17 tt G a, b a b a 0 b 0 W H S N x ft N C 0, σ s f zt + w f h t 18 X x ft 2 Exp σ s f zt + w f h t 19 x ft 2 x ft Exp λ λ 3. 4 VAE VAE S C F T p S p S Z p S = p S Z p Z dz p S Z DNN VAE Z q Z p S Z S q Z q Z = q z dt = N µ z 2 d st, σ z 2 d st 21 µ z d : RF + R σ z d : RF + R + DNN. log p S KL [q Z p Z ] + E q [log p S Z ] 22 { 1 µ z = d 2 st 2 } 2 + σ z d st 2 log σ z d st 2 [ + E q log σ s f zt s ] ft 2 σ s f zt + const. 23 f,t σ s f µz n σ z n SGD 3. 5 MCMC p W, H, Z X MCMC [20] MCMC - 3-3

4 Algorithm 1 VAE-NMF 1: for i = 1, 2, 3,... do 2: for = 1, 2, 3,..., K do 3: : 24 w = [w 1,..., w F ] T 5: : 25 h = [h 1,..., h T ] 7: end for 8: for t = 1, 2, 3,..., T do 9: 28 z t 10: end for 11: end for W H Z Algorithm 1 W H h t w f H, Z GIG a 0, b 0 +, λ ft w f h t W, Z GIG a 0, b 0 +, λ ft t f t f x ft 2 ϕ2 ft h t x ft 2 ϕ2 ft w f GIG γ, ρ, τ x γ 1 exp ρx τ/x γ ρ τ λ ft ϕ ft ϕ ft = w f h t w fh t + σ s f zt 26 λ ft = w f h t + σ s f zt 27 Z Metropolis-Hasting: MH z dt q z dt z dt = N z dt, σ 28 σ 3. 6 p S X, W, H, Z S S Ŝ C F T Ŝ ŝ ft = σ f z t w fh t + σ f z t x ft CHiME-3 Challenge [24] 4. 1 CHiME-3 BUS CAF PED STR 4 WSJ0 Signal-to-Noise Ratio: SNR CHiME-3 WSJ SNR 0 db 32 CHiME Hz Signal-to-Distortion Ratio: SDR [25] SDR MIR-EVAL [26] RNMF [27] RNMF X R F T + NMF S R F T + x ft w f h t + s ft 30 w f h t VAE-NMF VAE RNMF VAE-NMF STFT NMF K 5 W H a 0 b 0 1.0, K/scale scale Z D 10 Z σ 0.01 VAE-NMF W H Z VAE 2 DNN p s t z t q z t s t 5 WSJ0 JNAS [28] WSJ0 15 WSJ0 WSJ0 VAE-NMF - 4-4

5 出力 1/σσ ff ss zz tt 513, Softplus 出力 μμ dd zz ss tt 10, 変換無出力 σσ dd zz ss tt 10, Softplus 出力 1/σσ ss ff zz tt 513, Softplus 入力 zz tt 10 a p s t z t 全結合層 512 x 5, ReLU 入力 ss tt 513 b q z t s t 2: DNN p s t z t q z t s t 1: SDR BUS CAF PED STR VAE-NMF WSJ VAE-NMF JNAS RNMF 全結合層 512 x 5, ReLU JNAS JNAS 23 SGD Adam [29] RNMF RNMF WSJ0 SDR 1.26 db JNAS SDR 1.80 db JNAS VAE-NMF WSJ0 SDR JNAS VAE-NMF SDR 3 VAE-NMF 4 Hz RNMF BUS RNMF VAE-NMF VAE-NMF CAF PED CAF PED VAE-NMF 5. 全結合層 512 x 5, ReLU VAE- NMF VAE-NMF 入力 zz tt 10 NMF VAE-NMF 5. 1 VAE VAE VAE [30] 5. 2 VAE VAE VAE-NMF NMF [31] VAE 6. NMF VAE VAE-NMF VAE- NMF VAE, NMF VAE SDR No. 15J08765 ImPACT - 5-5

8 BUS CAF PED STR Freq. [Hz] 4 0 8 Freq. [Hz] 4 0 8 Freq. [Hz] 4 0 3: VAE-NMF WSJ0 RNMF [1] J. Heymann et al.

Speech enhancement based on deep denoising autoencoder. In Interspeech, pages 436 440, 2013. [3] Y. Ephraim et al.

Supervised and unsupervised speech enhancement using nonnegative matrix factorization. IEEE TASLP, 2110:2140 2151, 2013. [5] Y. Li et al.

Spatial correlation model based observation vector clustering and MVDR beamforming for meeting recognition. In IEEE ICASSP, pages 385 389, 2016. [7] N. Ono.

Phase-optimized K-SVD for signal extraction from underdetermined multichannel sparse mixtures. In IEEE ICASSP, pages 355 359, 2015. [9] P. C. Loizou.

[11] Z. Chen et al. Speech enhancement by sparse, low-ran, and dictionary spectrogram decomposition. In IEEE WASPAA, pages 1 4, 2013. [12] M. D. Hoffman.

Reduction of non-stationary noise for a robotic living assistant using sparse non-negative matrix factorization. In SMIAE, pages 28 33, 2012. [14] A. T. Cemgil.

Nonlinear hyperspectral unmixing with robust nonnegative matrix factorization. IEEE TSP, 2412:4810 4819, 2015. [16] N. Dobigeon et al.

Speech enhancement under low SNR conditions via noise estimation using sparse and low-ran NMF with Kullbac Leibler divergence. IEEE/ACM TASLP, 237:1233 1242, 2015.

M. Bishop. Pattern recognition. Machine Learning, 128, 2006. [21] I. Goodfellow et al. Generative adversarial nets. In NIPS, pages 2672 2680, 2014. [22] A.

Voice conversion from unaligned corpora using variational autoencoding wasserstein generative adversarial networs. arxiv:1704.00849, 2017. [24] J. Barer et al.

Performance measurement in blind audio source separation. IEEE TASLP, 144:1462 1469, 2006. [26] C. Raffel et al.

6 8 BUS CAF PED STR Freq. [Hz] Freq. [Hz] Freq. [Hz] 4 0 3: VAE-NMF WSJ0 RNMF [1] J. Heymann et al. Neural networ based spectral mas estimation for acoustic beamforming. In IEEE ICASSP, pages , [2] X. Lu et al. Speech enhancement based on deep denoising autoencoder. In Interspeech, pages , [3] Y. Ephraim et al. Speech enhancement using a minimummean square error short-time spectral amplitude estimator. IEEE TASLP, 326: , [4] N. Mohammadiha et al. Supervised and unsupervised speech enhancement using nonnegative matrix factorization. IEEE TASLP, 2110: , [5] Y. Li et al. Speech enhancement based on robust NMF solved by alternating direction method of multipliers. In IEEE MMSP, pages 1 5, [6] S. Arai et al. Spatial correlation model based observation vector clustering and MVDR beamforming for meeting recognition. In IEEE ICASSP, pages , [7] N. Ono. Stable and fast update rules for independent vector analysis based on auxiliary function technique. In IEEE WASPAA, pages , [8] Antoine Deleforge et al. Phase-optimized K-SVD for signal extraction from underdetermined multichannel sparse mixtures. In IEEE ICASSP, pages , [9] P. C. Loizou. Speech enhancement: theory and practice. CRC press, [10] C. Sun et al. Noise reduction based on robust principal component analysis. JCIS, 1010: , [11] Z. Chen et al. Speech enhancement by sparse, low-ran, and dictionary spectrogram decomposition. In IEEE WASPAA, pages 1 4, [12] M. D. Hoffman. Poisson-uniform nonnegative matrix factorization. In IEEE ICASSP, pages , [13] B. Cauchi et al. Reduction of non-stationary noise for a robotic living assistant using sparse non-negative matrix factorization. In SMIAE, pages 28 33, [14] A. T. Cemgil. Bayesian inference for nonnegative matrix factorisation models. CIN, :1 17, [15] C. Févotte et al. Nonlinear hyperspectral unmixing with robust nonnegative matrix factorization. IEEE TSP, 2412: , [16] N. Dobigeon et al. Robust nonnegative matrix factorization for nonlinear unmixing of hyperspectral images. In WHIS- PERS, pages 1 4, [17] M. Sun et al. Speech enhancement under low SNR conditions via noise estimation using sparse and low-ran NMF with Kullbac Leibler divergence. IEEE/ACM TASLP, 237: , [18] D. P. Kingma et al. Auto-encoding variational bayes. arxiv: , [19] C. Doersch. Tutorial on variational autoencoders. arxiv: , [20] C. M. Bishop. Pattern recognition. Machine Learning, 128, [21] I. Goodfellow et al. Generative adversarial nets. In NIPS, pages , [22] A. Radford et al. Unsupervised representation learning with deep convolutional generative adversarial networs. arxiv: , [23] C. Hsu et al. Voice conversion from unaligned corpora using variational autoencoding wasserstein generative adversarial networs. arxiv: , [24] J. Barer et al. The third CHiME speech separation and recognition challenge: Dataset, tas and baselines. In IEEE ASRU, pages , [25] E. Vincent et al. Performance measurement in blind audio source separation. IEEE TASLP, 144: , [26] C. Raffel et al. mir eval: a transparent implementation of common MIR metrics. In ISMIR, pages , [27] Y. Bando et al. Variational Bayesian multi-channel robust NMF for human-voice enhancement with a deformable and partially-occluded microphone array. In EUSIPCO, pages , [28] K. Itou et al. The design of the newspaper-based Japanese large vocabulary continuous speech recognition corpus. In ICSLP, [29] D. Kingma et al. Adam: A method for stochastic optimization. arxiv: , [30] O. Fabius et al. Variational recurrent auto-encoders. arxiv: , [31] K. Itaura et al. Bayesian multichannel nonnegative matrix factorization for audio source separation and localization. In IEEE ICASSP, pages ,

力出力 ÝÒ 源分離 f å 2 š ž 伸縮率 f g å ² f œå 1 ( F0) audio-to-audio 3 2 RNMF [2] DTW audio-to-audio [3] [4] MIDI 2.2 [5 10] Dannenberg [5] Verc

力出力 ÝÒ 源分離 f å 2 š ž 伸縮率 f g å ² f œå 1 ( F0) audio-to-audio 3 2 RNMF [2] DTW audio-to-audio [3] [4] MIDI 2.2 [5 10] Dannenberg [5] Verc 1,a) 1,b) 1,c) 1,d) 2,e) (MIDI ) audio-to-audio (RNMF) (DTW) DTW 1., (MIDI ) MIDI CD 2 1 1 MIDI CGM (Consumer Generated Music) Web Songrium [1] 2007 7 120 Web 1 2 / AIP a) wada@sap.ist.i.kyoto-u.ac.jp