On the Difference Between the Information Bottleneck and the Deep Information Bottleneck

Combining the Information Bottleneck model with deep learning by replacing mutual information terms with deep neural nets has proved successful in areas ranging from generative modelling to interpreting deep neural networks. In this paper, we revisit the Deep Variational Information Bottleneck and the assumptions needed for its derivation. The two assumed properties of the data $X$, $Y$ and their latent representation $T$ take the form of two Markov chains $T-X-Y$ and $X-T-Y$. Requiring both to hold during the optimisation process can be limiting for the set of potential joint distributions $P(X,Y,T)$. We therefore show how to circumvent this limitation by optimising a lower bound for $I(T;Y)$ for which only the latter Markov chain has to be satisfied. The actual mutual information consists of the lower bound which is optimised in DVIB and cognate models in practice and of two terms measuring how much the former requirement $T-X-Y$ is violated. Finally, we propose to interpret the family of information bottleneck models as directed graphical models and show that in this framework the original and deep information bottlenecks are special cases of a fundamental IB model

Informed MCMC with Bayesian Neural Networks for Facial Image Analysis

Computer vision tasks are difficult because of the large variability in the data that is induced by changes in light, background, partial occlusion as well as the varying pose, texture, and shape of objects. Generative approaches to computer vision allow us to overcome this difficulty by explicitly modeling the physical image formation process. Using generative object models, the analysis of an observed image is performed via Bayesian inference of the posterior distribution. This conceptually simple approach tends to fail in practice because of several difficulties stemming from sampling the posterior distribution: high-dimensionality and multi-modality of the posterior distribution as well as expensive simulation of the rendering process. The main difficulty of sampling approaches in a computer vision context is choosing the proposal distribution accurately so that maxima of the posterior are explored early and the algorithm quickly converges to a valid image interpretation. In this work, we propose to use a Bayesian Neural Network for estimating an image dependent proposal distribution. Compared to a standard Gaussian random walk proposal, this accelerates the sampler in finding regions of the posterior with high value. In this way, we can significantly reduce the number of samples needed to perform facial image analysis.Comment: Accepted to the Bayesian Deep Learning Workshop at NeurIPS 201

Learning Sparse Latent Representations with the Deep Copula Information Bottleneck

Deep latent variable models are powerful tools for representation learning. In this paper, we adopt the deep information bottleneck model, identify its shortcomings and propose a model that circumvents them. To this end, we apply a copula transformation which, by restoring the invariance properties of the information bottleneck method, leads to disentanglement of the features in the latent space. Building on that, we show how this transformation translates to sparsity of the latent space in the new model. We evaluate our method on artificial and real data.Comment: Published as a conference paper at ICLR 2018. Aleksander Wieczorek and Mario Wieser contributed equally to this wor

CHANGES IN THE ANAEROBIC THRESHOLD IN AN ANNUAL CYCLE OF SPORT TRAINING OF YOUNG SOCCER PLAYERS

The aim of the study was to assess changes in the anaerobic threshold of young soccer players in an annual training cycle. A group of highly trained 15-18 year old players of KKS Lech Poznań were tested. The tests included an annual training macrocycle, and its individual stages resulted from the time structure of the sports training. In order to assess the level of exercise capacities of the players, a field exercise test of increasing intensity was carried out on a soccer pitch. The test made it possible to determine the 4 millimolar lactate threshold (T LA 4 mmol · l-1) on the basis of the lactate concentration in blood [LA], to establish the threshold running speed and the threshold heart rate [HR]. The threshold running speed at the level of the 4 millimolar lactate threshold was established using the two-point form of the equation of a straight line. The obtained indicators of the threshold running speed allowed for precise establishment of effort intensity used in individual training in developing aerobic endurance. In order to test the significance of differences in mean values between four dates of tests, a non-parametric Friedman ANOVA test was used. The significance of differences between consecutive dates of tests was determined using a post-hoc Friedman ANOVA test. The tests showed significant differences in values of selected indicators determined at the anaerobic threshold in various stages of an annual training cycle of young soccer players. The most beneficial changes in terms of the threshold running speed were noted on the fourth date of tests, when the participants had the highest values of 4.01 m · s-1 for older juniors, and 3.80 m · s-1 for younger juniors. This may be indicative of effective application of an individualized programme of training loads and of good preparation of teams for competition in terms of players’ aerobic endurance

Critical level policies in lost sales inventory systems with different demand classes

We consider a single-item lost sales inventory model with different classes of customers. Each customer class may have different lost sale penalty costs. We assume that the demands follow a Poisson process and we consider a single replenishment hypoexponential server. We give a Markov decision process associated with this optimal control problem and prove some structural properties of its dynamic programming operator. This allows us to show that the optimal policy is a critical level policy. We then discuss some possible extensions to other replenishment distributions and give some numerical results for the hyperexponential server case

Myofascial Trigger Points Therapy Modifies Thermal Map of Gluteal Region

Background. (ermal imaging may be effectively used in musculoskeletal system diagnostics and therapy evaluation; thus, it may be successfully applied in myofascial trigger points assessment. Objective. Investigation of thermal pattern changes after myofascial trigger points progressive compression therapy in healthy males and females. Methods. (e study included 30 healthy people (15 females and 15 males) with age range 19–34 years (mean age: 23.1 ± 4.21). (ermograms of myofascial trigger points were taken pre- and posttherapy and consecutively in the 15th and 30th minutes. Pain reproducible by palpation intensity was assessed with numeric rating scale. Results. Progressive compression therapy leads to myofascial trigger points temperature (p 0.02) and surface (p 0.01) in males. In females no statistically significant changes were observed. Manual treatment leads to a decrease in intensity of pain reproducible by palpation in males (p 0.03) and females (p 0.048). Conclusions. (e study indicates that myofascial trigger points reaction to applied therapy spreads in time and space and depends on participants’ sex