Bayesian analysis of Ecological Momentary Assessment (EMA) data collected in adults before and after hearing rehabilitation.

This paper presents a new Bayesian method for analyzing Ecological Momentary Assessment (EMA) data and applies this method in a re-analysis of data from a previous EMA study. The analysis method has been implemented as a freely available Python package EmaCalc, RRID:SCR 022943. The analysis model can use EMA input data including nominal categories in one or more situation dimensions, and ordinal ratings of several perceptual attributes. The analysis uses a variant of ordinal regression to estimate the statistical relation between these variables. The Bayesian method has no requirements related to the number of participants or the number of assessments by each participant. Instead, the method automatically includes measures of the statistical credibility of all analysis results, for the given amount of data. For the previously collected EMA data, the analysis results demonstrate how the new tool can handle heavily skewed, scarce, and clustered data that were collected on ordinal scales, and present results on interval scales. The new method revealed results for the population mean that were similar to those obtained in the previous analysis by an advanced regression model. The Bayesian approach automatically estimated the inter-individual variability in the population, based on the study sample, and could show some statistically credible intervention results also for an unseen random individual in the population. Such results may be interesting, for example, if the EMA methodology is used by a hearing-aid manufacturer in a study to predict the success of a new signal-processing method among future potential customers.

Analysis of data from the International Outcome Inventory for Hearing Aids (IOI-HA) using Bayesian Item Response Theory.

OBJECTIVE: IOI-HA response data are conventionally analysed assuming that the ordinal responses have interval-scale properties. This study critically considers this assumption and compares the conventional approach with a method using Item Response Theory (IRT). DESIGN: A Bayesian IRT analysis model was implemented and applied to several IOI-HA data sets. STUDY SAMPLE: Anonymised IOI-HA responses from 13273 adult users of one or two hearing aids in 11 data sets using the Australian English, Dutch, German and Swedish versions of the IOI-HA. RESULTS: The raw ordinal responses to IOI-HA items do not represent values on interval scales. Using the conventional rating sum as an overall score introduces a scale error corresponding to about 10 - 15% of the true standard deviation in the population. Some interesting and statistically credible differences were demonstrated among the included data sets. CONCLUSIONS: It is questionable to apply conventional statistical measures like mean, variance, t-tests, etc., on the raw IOI-HA ratings. It is recommended to apply only nonparametric statistical test methods for comparisons of IOI-HA results between groups. The scale error can sometimes cause incorrect conclusions when individual results are compared. The IRT approach is recommended for analysis of individual results.

Bayesian analysis of paired-comparison sound quality ratings.

This paper presents a method to analyze paired-comparison data including either binary or graded ordinal responses, with or without ties. The proposed method can use either of two classical choice models: (1) Thurstone case V, which assumes a Gaussian distribution of the sensory variables underlying listener decisions, or (2) the Bradley-Terry-Luce (BTL) model, which assumes a logistic distribution. The analysis method was validated using simulated paired-comparison experiments with known distributions of the sound-quality parameters in the simulated population from which "participants" were generated at random. The validation indicated that the Thurstone and BTL models give similar results close to the true values. The estimated credibility of a quality difference was slightly higher with the BTL model. The analysis results showed dramatically better precision when the response data included graded ordinal judgments instead of binary responses. Allowing tied responses also tended to improve precision. The method was also applied to data from a real evaluation of hearing-aid programs. The analysis revealed clinically interesting results with high statistical credibility, although the amount of test data was limited.

Decorrelation of Neutral Vector Variables: Theory and Applications.

In this paper, we propose novel strategies for neutral vector variable decorrelation. Two fundamental invertible transformations, namely, serial nonlinear transformation and parallel nonlinear transformation, are proposed to carry out the decorrelation. For a neutral vector variable, which is not multivariate-Gaussian distributed, the conventional principal component analysis cannot yield mutually independent scalar variables. With the two proposed transformations, a highly negatively correlated neutral vector can be transformed to a set of mutually independent scalar variables with the same degrees of freedom. We also evaluate the decorrelation performances for the vectors generated from a single Dirichlet distribution and a mixture of Dirichlet distributions. The mutual independence is verified with the distance correlation measurement. The advantages of the proposed decorrelation strategies are intensively studied and demonstrated with synthesized data and practical application evaluations.

Variational Inference for Watson Mixture Model.

This paper addresses modelling data using the Watson distribution. The Watson distribution is one of the simplest distributions for analyzing axially symmetric data. This distribution has gained some attention in recent years due to its modeling capability. However, its Bayesian inference is fairly understudied due to difficulty in handling the normalization factor. Recent development of Markov chain Monte Carlo (MCMC) sampling methods can be applied for this purpose. However, these methods can be prohibitively slow for practical applications. A deterministic alternative is provided by variational methods that convert inference problems into optimization problems. In this paper, we present a variational inference for Watson mixture models. First, the variational framework is used to side-step the intractability arising from the coupling of latent states and parameters. Second, the variational free energy is further lower bounded in order to avoid intractable moment computation. The proposed approach provides a lower bound on the log marginal likelihood and retains distributional information over all parameters. Moreover, we show that it can regulate its own complexity by pruning unnecessary mixture components while avoiding over-fitting. We discuss potential applications of the modeling with Watson distributions in the problem of blind source separation, and clustering gene expression data sets.

Variational Bayesian Matrix Factorization for Bounded Support Data.

A novel Bayesian matrix factorization method for bounded support data is presented. Each entry in the observation matrix is assumed to be beta distributed. As the beta distribution has two parameters, two parameter matrices can be obtained, which matrices contain only nonnegative values. In order to provide low-rank matrix factorization, the nonnegative matrix factorization (NMF) technique is applied. Furthermore, each entry in the factorized matrices, i.e., the basis and excitation matrices, is assigned with gamma prior. Therefore, we name this method as beta-gamma NMF (BG-NMF). Due to the integral expression of the gamma function, estimation of the posterior distribution in the BG-NMF model can not be presented by an analytically tractable solution. With the variational inference framework and the relative convexity property of the log-inverse-beta function, we propose a new lower-bound to approximate the objective function. With this new lower-bound, we derive an analytically tractable solution to approximately calculate the posterior distributions. Each of the approximated posterior distributions is also gamma distributed, which retains the conjugacy of the Bayesian estimation. In addition, a sparse BG-NMF can be obtained by including a sparseness constraint to the gamma prior. Evaluations with synthetic data and real life data demonstrate the good performance of the proposed method.

Comparison of predictive measures of speech recognition after noise reduction processing.

A number of measures were evaluated with regard to their ability to predict the speech-recognition benefit of single-channel noise reduction (NR) processing. Three NR algorithms and a reference condition were used in the evaluation. Twenty listeners with impaired hearing and ten listeners with normal hearing participated in a blinded laboratory study. An adaptive speech test was used. The speech test produces results in terms of signal-to-noise ratios that correspond to equal speech recognition performance (in this case 80% correct) with and without the NR algorithms. This facilitates a direct comparison between predicted and experimentally measured effects of noise reduction algorithms on speech recognition. The experimental results were used to evaluate nine different predictive measures, one in two variants. The best predictions were found with the Coherence Speech Intelligibility Index (CSII) [Kates and Arehart (2005), J. Acoust. Soc. Am. 117(4), 2224-2237]. In general, measures using correlation between the clean speech and the processed noisy speech, as well as other measures that are based on short-time analysis of speech and noise, seemed most promising.

Analysis of click-evoked auditory brainstem responses using time domain cross-correlations between interleaved responses.

OBJECTIVES: The rapidly evolving field of early diagnostics after the introduction of newborn hearing screening requires rapid, valid, and objective methods, which have to be thoroughly evaluated in adults before use in infants. The aim was to study cross-correlation analysis of interleaved auditory brainstem responses (ABRs) in a wide dynamic range in normal-hearing adults. Off-line analysis allowed for comparison with psychoacoustical click threshold (PCT), pure-tone threshold, and determination of ABR input/output function. Specifically, nonfiltered and band-pass filtered ABRs were studied in various time segments along with time elapsed for ensemble of sweeps reaching a specific detection criterion. DESIGN: Fourteen healthy normal-hearing subjects (18 to 35 years of age, 50% females) without any history of noise exposure participated. They all had pure-tone thresholds better than 20 dB HL (125 to 8000 Hz). ABRs were recorded in both ears using 100 µsec clicks, from 71.5 dB nHL down to -18.5 dB nHL, in 10 dB steps (repetition rate, 39 Hz; time window, 15 msec; filter, 30 to 8000 Hz). The number of sweeps increased from 2000 at 71.5 dB nHL, up to 30000 at -18.5 dB nHL. Each sweep was stored in a data base for off-line analysis. Cross-correlation analysis between two subaverages of interleaved responses was performed in the time domain for nonfiltered and digitally band-pass filtered (300 to 1500 Hz) entire and time-windowed (1 to 11 and 5 to 11 msec) responses. PCTs were measured using a Bekesy technique with the same insert phone and stimulus as used for the ABR (repetition rate, 20 Hz). Time elapsed (≈ number of accepted sweeps/repetition rate) for the ensemble of sweeps needed to reach a cross-correlation coefficient (ρ) of 0.70 (=3.7 dB signal-to-noise ratio [SNR]) was analyzed. RESULTS: Mean cross-correlation coefficients exceeded 0.90 in both ears at stimulus levels ≥11.5 dB nHL for the entire nonfiltered ABR. At 1.5 dB nHL, mean(SD) ρ was 0.53(0.32) and 0.44(0.40) for left and right ears, respectively (n = 14) (=0 dB SNR). In comparison, mean(SD) PCT was -1.9(2.9) and -2.5(3.2) dB nHL for left and right ears, respectively (n = 14), while mean pure-tone average (500 to 2000 Hz) was 2.5 dB HL (n = 28). Almost no effect of band-pass filtering or reduced analysis time window existed. Average time elapsed needed to reach ρ = 0.70 was approximately 20 seconds or less at stimulus levels ≥41.5 dB nHL, and ≈30 seconds at 31.5 dB nHL. The average (interpolated) stimulus level corresponding to ρ=0.70 for the entire nonfiltered ABR was 6.5 dB nHL (n = 28), which coincided with the estimated psychoacoustical threshold for single clicks. CONCLUSIONS: ABR could be identified in a short period of time using cross-correlation analysis between interleaved responses. The average stimulus level corresponding to 0 dB SNR in the entire nonfiltered ABR occurred at 1.5 dB nHL, 4 dB above the average PCT. The mean input/output function for the ensemble of sweeps required to reach ρ = 0.70 increased monotonically with increasing stimulus level, in parallel with the ABR based on all sweeps (≥1.5 dB nHL). Time domain cross-correlation analysis of ABR might form the basis for automatic response identification and future threshold-seeking procedures.

Bayesian Estimation of the von-Mises Fisher Mixture Model with Variational Inference.

This paper addresses the Bayesian estimation of the von-Mises Fisher (vMF) mixture model with variational inference (VI). The learning task in VI consists of optimization of the variational posterior distribution. However, the exact solution by VI does not lead to an analytically tractable solution due to the evaluation of intractable moments involving functional forms of the Bessel function in their arguments. To derive a closed-form solution, we further lower bound the evidence lower bound where the bound is tight at one point in the parameter distribution. While having the value of the bound guaranteed to increase during maximization, we derive an analytically tractable approximation to the posterior distribution which has the same functional form as the assigned prior distribution. The proposed algorithm requires no iterative numerical calculation in the re-estimation procedure, and it can potentially determine the model complexity and avoid the over-fitting problem associated with conventional approaches based on the expectation maximization. Moreover, we derive an analytically tractable approximation to the predictive density of the Bayesian mixture model of vMF distributions. The performance of the proposed approach is verified by experiments with both synthetic and real data.

Bayesian estimation of beta mixture models with variational inference.

Bayesian estimation of the parameters in beta mixture models (BMM) is analytically intractable. The numerical solutions to simulate the posterior distribution are available, but incur high computational cost. In this paper, we introduce an approximation to the prior/posterior distribution of the parameters in the beta distribution and propose an analytically tractable (closed form) Bayesian approach to the parameter estimation. The approach is based on the variational inference (VI) framework. Following the principles of the VI framework and utilizing the relative convexity bound, the extended factorized approximation method is applied to approximate the distribution of the parameters in BMM. In a fully Bayesian model where all of the parameters of the BMM are considered as variables and assigned proper distributions, our approach can asymptotically find the optimal estimate of the parameters posterior distribution. Also, the model complexity can be determined based on the data. The closed-form solution is proposed so that no iterative numerical calculation is required. Meanwhile, our approach avoids the drawback of overfitting in the conventional expectation maximization algorithm. The good performance of this approach is verified by experiments with both synthetic and real data.

Multicenter evaluation of signal enhancement algorithms for hearing aids.

In the framework of the European HearCom project, promising signal enhancement algorithms were developed and evaluated for future use in hearing instruments. To assess the algorithms' performance, five of the algorithms were selected and implemented on a common real-time hardware/software platform. Four test centers in Belgium, The Netherlands, Germany, and Switzerland perceptually evaluated the algorithms. Listening tests were performed with large numbers of normal-hearing and hearing-impaired subjects. Three perceptual measures were used: speech reception threshold (SRT), listening effort scaling, and preference rating. Tests were carried out in two types of rooms. Speech was presented in multitalker babble arriving from one or three loudspeakers. In a pseudo-diffuse noise scenario, only one algorithm, the spatially preprocessed speech-distortion-weighted multi-channel Wiener filtering, provided a SRT improvement relative to the unprocessed condition. Despite the general lack of improvement in SRT, some algorithms were preferred over the unprocessed condition at all tested signal-to-noise ratios (SNRs). These effects were found across different subject groups and test sites. The listening effort scores were less consistent over test sites. For the algorithms that did not affect speech intelligibility, a reduction in listening effort was observed at 0 dB SNR.

Preferred overall loudness. I: Sound field presentation in the laboratory.

This study questions the basic assumption that prescriptive methods for nonlinear, wide dynamic range compression (WDRC) hearing aids should restore overall loudness to normal. Fifteen normal-hearing listeners and twenty-four hearing-impaired listeners (with mild to moderate hearing loss, twelve with and twelve without hearing aid experience) participated in laboratory tests. The participants first watched and listened to video sequences and rated how loud and how interesting the situations were. For the hearing-impaired participants, gain was applied according to the NAL-NL1 prescription. Despite the fact that the NAL-NL1 prescription led to less than normal overall calculated loudness, according to the loudness model of Moore and Glasberg (1997), the hearing-impaired participants rated loudness higher than the normal-hearing participants. The participants then adjusted a volume control to preferred overall loudness. Both normal-hearing and hearing-impaired participants preferred less than normal overall calculated loudness. The results from the two groups of hearing-impaired listeners did not differ significantly.

Preferred overall loudness. II: Listening through hearing aids in field and laboratory tests.

In a laboratory study, we found that normal-hearing and hearing-impaired listeners preferred less than normal overall calculated loudness (according to a loudness model of Moore & Glasberg, 1997). The current study verified those results using a research hearing aid. Fifteen hearing-impaired and eight normal-hearing participants used the hearing aid in the field and adjusted a volume control to give preferred loudness. The hearing aid logged the preferred volume control setting and the calculated loudness at that setting. The hearing-impaired participants preferred, in median, loudness levels of -14 phon re normal for input levels from 50 to 89 dB SPL. The normal-hearing participants preferred close to normal overall loudness. In subsequent laboratory tests, using the same hearing aid, both hearing-impaired and normal-hearing listeners preferred less than normal overall calculated loudness, and larger reductions for higher input levels In summary, the hearing-impaired listeners preferred less than normal overall calculated loudness, whereas the results for the normal-hearing listeners were inconclusive.

Methodology for quantifying perceptual effects from noise suppression systems.

Methodology is proposed for perceptual assessment of both subjective sound quality and speech recognition in such way that results can be compared between these two aspects. Validation is performed with a noise suppression system applied to hearing instruments. A method termed Interpolated Paired Comparison Rating (IPCR) was developed for time efficient assessment of subjective impression of different aspects of sound quality for a variety of noise conditions. The method is based on paired comparisons between processed and unprocessed stimuli, and the results are expressed as the difference in signal-to-noise ratio (dB) between these that give equal subjective impression. For tests of speech recognition in noise, validated adaptive test methods can be used that give results in terms of speech-to-noise ratio. The methodology was shown to be sensitive enough to detect significant mean differences between processed and unprocessed speech in noise, both regarding subjective sound quality and speech recognition ability in groups consisting of 30 subjects. An effect on sound quality from the noise suppression equivalent to about 3-4 dB is required to be statistically significant for a single subject. A corresponding effect of 3-6 dB is required for speech recognition (one-sided test). The magnitude of difference that occurred in the present study for sound quality was sufficient to show significant differences for sound quality within individuals, but this was not the case for speech recognition.

Hearing-aid automatic gain control adapting to two sound sources in the environment, using three time constants.

A hearing aid AGC algorithm is presented that uses a richer representation of the sound environment than previous algorithms. The proposed algorithm is designed to (1) adapt slowly (in approximately 10 s) between different listening environments, e.g., when the user leaves a single talker lecture for a multi-babble coffee-break; (2) switch rapidly (about 100 ms) between different dominant sound sources within one listening situation, such as the change from the user's own voice to a distant speaker's voice in a quiet conference room; (3) instantly reduce gain for strong transient sounds and then quickly return to the previous gain setting; and (4) not change the gain in silent pauses but instead keep the gain setting of the previous sound source. An acoustic evaluation showed that the algorithm worked as intended. The algorithm was evaluated together with a reference algorithm in a pilot field test. When evaluated by nine users in a set of speech recognition tests, the algorithm showed similar results to the reference algorithm.

An efficient robust sound classification algorithm for hearing aids.

An efficient robust sound classification algorithm based on hidden Markov models is presented. The system would enable a hearing aid to automatically change its behavior for differing listening environments according to the user's preferences. This work attempts to distinguish between three listening environment categories: speech in traffic noise, speech in babble, and clean speech, regardless of the signal-to-noise ratio. The classifier uses only the modulation characteristics of the signal. The classifier ignores the absolute sound pressure level and the absolute spectrum shape, resulting in an algorithm that is robust against irrelevant acoustic variations. The measured classification hit rate was 96.7%-99.5% when the classifier was tested with sounds representing one of the three environment categories included in the classifier. False-alarm rates were 0.2%-1.7% in these tests. The algorithm is robust and efficient and consumes a small amount of instructions and memory. It is fully possible to implement the classifier in a DSP-based hearing instrument.

Multi-programmable Hearing Aid.

A basic problem in hearing-aid fitting is the difficulty in finding one setting optimal to all listening situations that might occur. The objective was to develop a behind-the-ear hearing-aid with a very flexible analog signal processor which is digitally controlled, and a memory with logic, so that the hearing-impaired person can select from eight completely different fittings. To program and adjust this multi-programmable hearing-aid (called MemoryMate®) a hearing evaluation and recommendation system (called Master-Fit®) has been developed, based on an IBM PS/2 computer. This system offers the dispenser prescriptive fitting methods and performance of real ear measurements. It can be used to manage a client database. Preliminary results from a clinical study conducted in 1988 are presented. The paper also describes the uniqueness of this multi-programmable hearing aid as a powerful new research tool.