H\"older-type inequalities and their applications to concentration and correlation bounds

Let $Y_v, v\in V,$ be $[0,1]$-valued random variables having a dependency graph $G=(V,E)$. We show that $$\mathbb{E}\left[\prod_{v\in V} Y_{v} \right] \leq \prod_{v\in V} \left\{ \mathbb{E}\left[Y_v^{\frac{\chi_b}{b}}\right] \right\}^{\frac{b}{\chi_b}},$$ where $\chi_b$ is the $b$-fold chromatic number of $G$. This inequality may be seen as a dependency-graph analogue of a generalised H\"older inequality, due to Helmut Finner. Additionally, we provide applications of H\"older-type inequalities to concentration and correlation bounds for sums of weakly dependent random variables.Comment: 15 page

Learning from networked examples

Many machine learning algorithms are based on the assumption that training examples are drawn independently. However, this assumption does not hold anymore when learning from a networked sample because two or more training examples may share some common objects, and hence share the features of these shared objects. We show that the classic approach of ignoring this problem potentially can have a harmful effect on the accuracy of statistics, and then consider alternatives. One of these is to only use independent examples, discarding other information. However, this is clearly suboptimal. We analyze sample error bounds in this networked setting, providing significantly improved results. An important component of our approach is formed by efficient sample weighting schemes, which leads to novel concentration inequalities

MIDI-VAE: Modeling Dynamics and Instrumentation of Music with Applications to Style Transfer

We introduce MIDI-VAE, a neural network model based on Variational Autoencoders that is capable of handling polyphonic music with multiple instrument tracks, as well as modeling the dynamics of music by incorporating note durations and velocities. We show that MIDI-VAE can perform style transfer on symbolic music by automatically changing pitches, dynamics and instruments of a music piece from, e.g., a Classical to a Jazz style. We evaluate the efficacy of the style transfer by training separate style validation classifiers. Our model can also interpolate between short pieces of music, produce medleys and create mixtures of entire songs. The interpolations smoothly change pitches, dynamics and instrumentation to create a harmonic bridge between two music pieces. To the best of our knowledge, this work represents the first successful attempt at applying neural style transfer to complete musical compositions.Comment: Paper accepted at the 19th International Society for Music Information Retrieval Conference, ISMIR 2018, Paris, Franc