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Permutation invariant training (PIT) is a widely used training criterion for neural network-based source separation, used for both utterance-level separation with utterance-level PIT (uPIT) and separation of long recordings with the recently proposed Graph-PIT. When implemented naively, both suffer from an exponential complexity in the number of utterances to separate, rendering them unusable for large numbers of speakers or long realistic recordings. We present a decomposition of the PIT criterion into the computation of a matrix and a strictly monotonously increasing function so that the permutation or assignment problem can be solved efficiently with several search algorithms. The Hungarian algorithm can be used for uPIT and we introduce various algorithms for the Graph-PIT assignment problem to reduce the complexity to be polynomial in the number of utterances.
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Single-microphone, speaker-independent speech separation is normally performed through two steps: (i) separating the specific speech sources, and (ii) determining the best output-label assignment to find the separation error. The second step is the main obstacle in training neural networks for speech separation. Recently proposed Permutation Invariant Training (PIT) addresses this problem by determining the output-label assignment which minimizes the separation error. In this study, we show that a major drawback of this technique is the overconfident choice of the output-label assignment, especially in the initial steps of training when the network generates unreliable outputs. To solve this problem, we propose Probabilistic PIT (Prob-PIT) which considers the output-label permutation as a discrete latent random variable with a uniform prior distribution. Prob-PIT defines a log-likelihood function based on the prior distributions and the separation errors of all permutations; it trains the speech separation networks by maximizing the log-likelihood function. Prob-PIT can be easily implemented by replacing the minimum function of PIT with a soft-minimum function. We evaluate our approach for speech separation on both TIMIT and CHiME datasets. The results show that the proposed method significantly outperforms PIT in terms of Signal to Distortion Ratio and Signal to Interference Ratio.
Automatic transcription of meetings requires handling of overlapped speech, which calls for continuous speech separation (CSS) systems. The uPIT criterion was proposed for utterance-level separation with neural networks and introduces the constraint that the total number of speakers must not exceed the number of output channels. When processing meeting-like data in a segment-wise manner, i.e., by separating overlapping segments independently and stitching adjacent segments to continuous output streams, this constraint has to be fulfilled for any segment. In this contribution, we show that this constraint can be significantly relaxed. We propose a novel graph-based PIT criterion, which casts the assignment of utterances to output channels in a graph coloring problem. It only requires that the number of concurrently active speakers must not exceed the number of output channels. As a consequence, the system can process an arbitrary number of speakers and arbitrarily long segments and thus can handle more diverse scenarios. Further, the stitching algorithm for obtaining a consistent output order in neighboring segments is of less importance and can even be eliminated completely, not the least reducing the computational effort. Experiments on meeting-style WSJ data show improvements in recognition performance over using the uPIT criterion.
We propose a block-online algorithm of guided source separation (GSS). GSS is a speech separation method that uses diarization information to update parameters of the generative model of observation signals. Previous studies have shown that GSS performs well in multi-talker scenarios. However, it requires a large amount of calculation time, which is an obstacle to the deployment of online applications. It is also a problem that the offline GSS is an utterance-wise algorithm so that it produces latency according to the length of the utterance. With the proposed algorithm, block-wise input samples and corresponding time annotations are concatenated with those in the preceding context and used to update the parameters. Using the context enables the algorithm to estimate time-frequency masks accurately only from one iteration of optimization for each block, and its latency does not depend on the utterance length but predetermined block length. It also reduces calculation cost by updating only the parameters of active speakers in each block and its context. Evaluation on the CHiME-6 corpus and a meeting corpus showed that the proposed algorithm achieved almost the same performance as the conventional offline GSS algorithm but with 32x faster calculation, which is sufficient for real-time applications.
Many applications of single channel source separation (SCSS) including automatic speech recognition (ASR), hearing aids etc. require an estimation of only one source from a mixture of many sources. Treating this special case as a regular SCSS problem where in all constituent sources are given equal priority in terms of reconstruction may result in a suboptimal separation performance. In this paper, we tackle the one source separation problem by suitably modifying the orthodox SCSS framework and focus only on one source at a time. The proposed approach is a generic framework that can be applied to any existing SCSS algorithm, improves performance, and scales well when there are more than two sources in the mixture unlike most existing SCSS methods. Additionally, existing SCSS algorithms rely on fine hyper-parameter tuning hence making them difficult to use in practice. Our framework takes a step towards automatic tuning of the hyper-parameters thereby making our method better suited for the mixture to be separated and thus practically more useful. We test our framework on a neural network based algorithm and the results show an improved performance in terms of SDR and SAR.
In neural network-based monaural speech separation techniques, it has been recently common to evaluate the loss using the permutation invariant training (PIT) loss. However, the ordinary PIT requires to try all $N!$ permutations between $N$ ground truths and $N$ estimates. Since the factorial complexity explodes very rapidly as $N$ increases, a PIT-based training works only when the number of source signals is small, such as $N = 2$ or $3$. To overcome this limitation, this paper proposes a SinkPIT, a novel variant of the PIT losses, which is much more efficient than the ordinary PIT loss when $N$ is large. The SinkPIT is based on Sinkhorns matrix balancing algorithm, which efficiently finds a doubly stochastic matrix which approximates the best permutation in a differentiable manner. The author conducted an experiment to train a neural network model to decompose a single-channel mixture into 10 sources using the SinkPIT, and obtained promising results.
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