Inconsistency of Bayesian Inference for Misspecified Linear Models, and a Proposal for Repairing It

We empirically show that Bayesian inference can be inconsistent under misspecification in simple linear regression problems, both in a model averaging/selection and in a Bayesian ridge regression setting. We use the standard linear model, which assumes homoskedasticity, whereas the data are heteroskedastic, and observe that the posterior puts its mass on ever more high-dimensional models as the sample size increases. To remedy the problem, we equip the likelihood in Bayes' theorem with an exponent called the learning rate, and we propose the Safe Bayesian method to learn the learning rate from the data. SafeBayes tends to select small learning rates as soon the standard posterior is not `cumulatively concentrated', and its results on our data are quite encouraging.Comment: 70 pages, 20 figure

Inconsistency of Bayesian inference for misspecified linear models, and a proposal for repairing it

We empirically show that Bayesian inference can be inconsistent under misspecification in simple linear regression problems, both in a model averaging/selection and in a Bayesian ridge regression setting. We use the standard linear model, which assumes homoskedasticity, whereas the data are heteroskedastic (though, significantly, there are no outliers). As sample size increases, the posterior puts its mass on worse and worse models of ever higher dimension. This is caused by hypercompression, the phenomenon that the posterior puts its mass on distributions that have much larger KL divergence from the ground truth than their average, i.e. the Bayes predictive distribution. To remedy the problem, we equip the likelihood in Bayes' theorem with an exponent called the learning rate, and we propose the SafeBayesian method to learn the learning rate from the data. SafeBayes tends to select small learning rates, and regularizes more, as soon as hypercompression takes place. Its results on our data are quite encouraging

A theoretic model for sonogenetic antiarrhythmia

Sonogenetics can be used as a new alternative for treating arrhythmia due to its advantages of noninvasive, high safety and strong penetration. In the treatment of arrhythmias by sonogenetics, cardiac myocytes are deformed by ultrasonic radiation force. We quantitatively calculated the shape variation of cardiomyocytes under ultrasonic radiation force, and the deformation of cardiomyocytes caused the change of membrane tension. Membrane tension consists of two parts, plasma membrane tension and cortical tension between the cell membrane and cytoskeleton. Since plasma membrane tension was mainly considered in existing experiments, we proposed a quantitative model of the relationship between ultrasonic radiation force and plasma membrane tension. The Boltzmann relationship between plasma membrane tension and ion channel opening probability is presented based on the experimental results of ion channel activation by stretching. Finally, a quantitative model was obtained for ultrasonic radiation force to regulate the opening probability of ion channel activated by stretching. Based on this quantitative model, we proposed the regulation mechanism of ultrasonic radiation force under hypercompression and hyperstretching, and verified that this mechanism can eliminate arrhythmias by sonogenetics.Comment: 13pages,5 figure

ANALIZA ZASTOSOWANIA FILTRÓW WSZECHPRZEPUSTOWYCH DO ELIMINACJI NEGATYWNYCH SKUTKÓW TENDENCJI LOUDNESS WAR

In this paper the influence of all-pass filters on musical material with applied hypercompression dynamics (loudness war trend) was analyzed. These filters are characterized by shifting phase in selected frequency band of signal, not by change of their amplitude levels. Because a lot of music information is present in music tracks, the dynamic range was tested together with influence of other sound parameters like selectivity or instruments’ arrangement on scene, by running subjective tests on a group of respondents.W artykule przeanalizowana wpływ filtrów wszechprzepustowych na materiał muzyczny z zastosowaną hiperkompresją sygnału (tendencją loudness war). Filtry tego typu, charakteryzują się przesunięciem w fazie składowych częstotliwościowych, sygnału, a nie zmianą poziomu ich amplitudy. Ze względu na dużą ilość informacji w utworach muzycznych, prócz sprawdzenia zakresu dynamiki poprzez testy obiektywne, zbadano również wpływ na inne parametry dźwięku takie jak selektywność czy rozłożenie instrumentów na scenie, poprzez testy subiektywne na grupie respondentów. &nbsp

Telling Cause from Effect using MDL-based Local and Global Regression

We consider the fundamental problem of inferring the causal direction between two univariate numeric random variables $X$ and $Y$ from observational data. The two-variable case is especially difficult to solve since it is not possible to use standard conditional independence tests between the variables. To tackle this problem, we follow an information theoretic approach based on Kolmogorov complexity and use the Minimum Description Length (MDL) principle to provide a practical solution. In particular, we propose a compression scheme to encode local and global functional relations using MDL-based regression. We infer $X$ causes $Y$ in case it is shorter to describe $Y$ as a function of $X$ than the inverse direction. In addition, we introduce Slope, an efficient linear-time algorithm that through thorough empirical evaluation on both synthetic and real world data we show outperforms the state of the art by a wide margin.Comment: 10 pages, To appear in ICDM1