To calculate word level confidence score Kaldi uses a method called MBR Decoding. MBR Decoding is a decoding process that minimize word level error rate (instead of minimizing the whole utterance cost) to calculate the result. This may not give the accurate result but can be use to calculate the confidence score up to some level. Just don’t expect too much as the performance is not well-accurate.

Here are some key concepts:

**1. Levenshtein Distance**: Levenshtein Distance or Edit Distance compute difference between two sentences. It computes how many words are different between the two. Lets say X and Y are two word sequence shown below. The Levenshtein distance would be 3 where Ɛ represent empty word

To calculate the Levenshtein distance you can use following recursive algorithm where A and B are word sequence with length of N+1

As in all recursive algorithm to decrease amount of duplicate computation Kaldi used the memoization technique and store the above three circumstances in a1, a2 and a3 respectively

**2. Forward-Backward Algorithm:** Lets say you want to calculate the probability of seeing a waveform(or MFCC features) given a path in a lattice (or on HHM FST). Then the Forward-Backward Algorithm is nothing more than a optimized way to compute this probability.

**3. Gamma Calculation: **TBA

**4. MBR Decoding: **TBA

Delta-Delta feature is proposed in 1986 by S. Furui and Hermann Ney in 1990. It’s simply add first and second derivative of cepstrum to the feature vector. By doing that they say it can capture spectral dynamics and improve overall accuracy.

The only problem is that in a discrete signal space getting derivative from the signal increase spontaneous noise level so instead of simple first and second order derivative HTK proposed a `differentiation filter`

. This filter basically is a convoluted low-pass filter on top of discrete signal derivative to smooth out the result and remove unwanted noises. In Fig 1 you can see the result of simple second derivative vs the proposed `differentiation filter`

.

HTK filter for a Delta-Delta feature (order=2, window=2) is a 9 element FIR filter with following coefficient(Θ is window size which is 2 in HTK)

• Reverberation: |
Is the effect of sound bouncing the walls and getting back in a room. The time is roughly between 1 and 2 second in an ordinary room. You can use `Sabine equation` to do more accurate calculation. |

- I’m thinking about using using
`compressor filter`

in speech instead of`CMVN`

to normalize in real-time.

- The above formula c_t makes no sense. I will update this as soon as I can post codes here

IEEE ICASSP ’86 – Isolated Word Recognition Based on Emphasized Spectral Dynamics

IEEE ICASSP ’90 – Experiments on mixture-density phoneme-modelling for 1000-word DARPA task

Desh Raj Blog – Award-winning classic papers in ML and NLP

• Lattices: |
Are a graph containing `states` (nodes) and `arcs` (edges). which each state represent one 10ms frame |

• Arcs: |
Are start from one state to another state. Each state arcs can be accessed with arc iterator and arcs only retain their next state. each arcs have weight and input and output label. |

• States: |
Are simple decimal number starting from `lat.Start()` . and goes up to `lat.NumStates()` . Most of the time start is 0 |

• Topological Sort: |
An FST is `topological sorted` if the FST can be laid out on a horizontal axis and no arc direction would be from right to left |

• Note 1: |
You can get max state with `lat.NumStates()` |

• Note 2: |
You can prune lattices by creating dead end path. Dead end path is a path that’s not get end up to the final state. After that `fst::connect` will trim the FST and get rid of these dead paths |

• Link: |
Same as arc |

• Token: |
Are same as state. They have costs |

• FrameToks: |
A link list that contain all tokens in a single frame |

• Adaptive Beam: |
Used in pruning before creating lattice and through decoding |

• NEmitting Tokens: |
Non Emitting Tokens or NEmitting Tokens are tokens that generate from emitting token in the same frame and have `input label = 0` and have `acoustic_cost = 0` |

• Emitting Tokens: |
Emitting Tokens are tokens that surpass from a frame to another frame |

A Simplified Block Diagram of ASR Process in Kaldi

• Costs: |
Are Log Negative Probability, so a higher cost means lower probability. |

• Frame: |
Each 10ms of audio that using MFCC turned into a fixed size vector called a frame. |

• Beam: |
Cutoff would be `Best Cost` –`Beam` (Around 10 to 16) |

• Cutoff: |
The maximum cost that all cost higher than this value will not be processed and removed. |

• Epsilon: |
The zero label in `FST` are called `<eps>` |

• Lattices: |
Are the same as FSTs, instead each token keeps in a framed based array called`frame_toks` . In This way the distance in time between each token will be perceived too. |

• Rescoring: |
A language model scoring system that applied after final state to improve final result by using stronger LM model than `n-gram` . |

• HCLG(FST): |
The main FST used in the decoding. The iLabel in this FST is TransitionIDs. |

• Model(MDL): |
A model that used to convert sound into acoustic cost and TransitionIDs. |

• TransitionIDs: |
A number that contain information about state and corresponding PDF id. |

• Emiting States: |
States that have pdfs associated with them and emit phoneme. In other word states that have their `ilabel` is not zero |

• Bakis Model: |
Is a HMM that state transitions proceed from left to right. In a Bakis HMM, no transitions go from a higher-numbered state to a lower-numbered state. |

• Max Active: |
Uses to calculate cutoff to determince maximum number of tokens that will be processed inside emitting process. |

• Graph Cost: |
is a sum of the LM cost, the (weighted) transition probabilities, and any pronunciation cost. |

• Acoustic Cost: |
Cost that is got from the decodable object. |

• Acoustic Scale: |
A floating number that multiply in all Log Likelihood (inside the decodable object). |

Fig. 1. Demonstration of Finite State Automata vs Lattices, Courtesy of Peter F. Brown

- Stanford University – Speech and Language Processing Book
- IEEE ICASSP – Partial traceback and dynamic programming

The command below generates a tone signal out of the speaker and receives it back through the mic. Measuring the phase diff will reveal the round-trip latency.

`alsa_delay hw:1,0 hw:0,0 44100 256 2 1 1`

Here `hw:1,0`

refer to the recording device that can be retrieved from `arecord -l`

and `hw:0,0`

refer to the playback device. Again can be retrieved from `aplay -l`

.

The `44100`

is the sampling rate. `256`

is the buffer size. `256`

works best for me. Lower numbers corrupt the test and higher numbers just bring more latency to the table. Don’t know exactly what `nfrags`

`input`

and `output`

arguments are but `2`

`1`

and `1`

respectively works magically for me. I just tinkering around and found these numbers. No other number works for me.

1. Focusrite Scarlett Solo Latency: *2.5ms *

2. Shure SM57 Mic Latency: *2.5ms*

3. OverAll Delay: 14ms with non-RT mode

You can tinker around the effect of latency with

`pactl load-module module-loopback latency_msec=15`

To end the loopback mode

`pactl unload-module module-loopback`

As Always Useful links

Arun Raghavan – Beamforming in PulseAudio

Arch Linux Wiki – Professional Audio, Realtime kernel

Let’s Enhance Kaldi, Here are some links along the way. Look like YouTube is progressing a lot during the last couple of years so basically here is just a bunch of random videos creating my favorite playlist to learn all the cool stuff under the Kaldi’s hood.

- Keith Chugg (USC) – Viterbi Algorithm
- Lim Zhi Hao (NTU) – WFST: A Nice Channel On Weighted Finite State Transducers
- Dan Povey (JHU) – ICASSP 2011 Kaldi Workshop: Dan Explaining Kaldi Basics
- Luis Serrano – The Covariance Matrix: To Understand GMM Acoustic Modeling

- Mehryar Mohri (NYU) – Speech Recognition with WFST: A joint work of RWTH and NYU
- Mehryar Mohri (NYU), Afshin Rostamizadeh – Foundations of Machine Learning
- George Doddington (US DoD) ICASSP 2011 – Human Assisted Speaker Recognition
- GitHub Kaldi – TED-LIUM Result: GMM, SGMM, Triple Deltas Comparison
- EE Columbia University – Speech Recognition Spring 2016
- D. Povey – Generating Lattices in the WFST : For understanding
`LattceFasterDecoder`

`Lattices`

: A more complex form of`FST`

‘s, The first version decoders were based on FST’s (like`faster-decoder`

and`online`

decoders). For Minimum Bayesian Risk Calculation Using`Lattices`

will give you a better paved way`faster-decoder`

: Old decoder, very simple to understand how decoding process is done`lattice-faster-decoder`

: general decoder, same as`faster-decoder`

but output lattices instead of`FST`

s`DecodableInterface`

: An interface that connects decoder to the features. decoder uses this`Decodable`

object to pull CMVN features from it.`BestPath`

: An FST that constructed from the Best Path (path with maximum likelihood) in the decoded FST.`nBestPath`

: An FST constructed from the top N Best Path in the decoded FST.`GetLinearSymbolSequence`

: The final step in the recognition process, get a BestPath FST or Lattice and output the recognized words with the path weight.`CompactLattice`

s need to be converted using`ConvertLattice`

`Strongly Connected Component`

: A set that all components are accessible (in two ways) by it’s member.- The Main Function in Decoder is
`ProcessEmitting`

that pulls`loglikelihood`

from the`decodable`

object

Thanks to this marvelous framework, a trained model is at disposal with WER of absolute zero percent over the 10 minutes of continuous speech file. The final piece to this puzzle would be implementing a semi-online decoding tool using GStreamer. As always useful links for further inspection

- GStreamer – Dynamic pipelines
- Function that save lives!
`gst_caps_to_string(caps)`

- GStreamer – GstBufferPool
- StackOverFlow – Gstreamer gst_buffer_pool_acquire_buffer function is slow on ARM
- GitHub – Alumae: GST-Kaldi-NNet2-Online
- StackOverFlow – How to create GstBuffer

Here I am, pursuing once more the old-fashioned machine learning. I’ll keep it short and write down useful links

- Hannes van Lier – Basic Introduction to Speech Recognition (HMM & Neural Networks)
- Luis Serrano – A friendly introduction to Bayes Theorem and Hidden Markov Models
- Djp3 – Hidden Markov Models, The forward-backward algorithm

- Kaldi ASR – FrameWork Wiki
- Kaldi Wiki – Kaldi Tutorial #1
- Dan Povey’s Homepage: Former Professor at John Hopkins University, Author of HTK Book
- KalDi WiKi – Kaldi for Dummies tutorial

- Wikipedia – Dempster–Shafer theory
- Wikipedia – Expectation–maximization algorithm
- Wikipedia – Cepstral mean and variance normalization
- Wikipedia – Baum–Welch algorithm
- Wikipedia – Mutual Information

- Medium – Jonathan Hui: ASR Model Training
- Medium – Jonathan Hui: Maximum Mutual Information Estimation (MMIE)
- Medium – Jonathan Hui: Weighted Finite-State Transducers

- LVCSR: Large Vocabulary Continuous Speech Recognition

Tags: Speech Recognition