We propose a simple and efficient method for ranking features in multi-label classification. The method produces a ranking of features showing their relevance in predicting labels, which in turn allows to choose a final subset of features. The procedure is based on Markov Networks and allows to model the dependencies between labels and features in a direct way. In the first step we build a simple network using only labels and then we test how much adding a single feature affects the initial network. More specifically, in the first step we use the Ising model whereas the second step is based on the score statistic, which allows to test a significance of added features very quickly. The proposed approach does not require transformation of label space, gives interpretable results and allows for attractive visualization of dependency structure. We give a theoretical justification of the procedure by discussing some theoretical properties of the Ising model and the score statistic. Numerical experiments show that the proposed methods outperform the conventional approaches on the considered artificial and real datasets. Introduction Multi-label classification (MLC) has recently attracted a significant attention, motivated by an increasing number of applications. More examples can be found in [22], [23] and [24]. The key problem in multi-label learning is how to utilize label dependencies to improve the classification performance, motivated by which number of multi-label algorithms have been proposed in recent years (see [25] for extensive comparison of several methods). The recent progress in MLC is summarized in [26] and [22]. In MLC, each object of our interest (e.g. One of the trending challenges in MLC is a dimensionality reduction of the feature space [22], i.e. reducing the dimensionality of the vector x. Usually only some features affect y.

We introduce a wavelet-domain functional analysis of variance (fANOVA) method based on a Bayesian hierarchical model. The factor effects are modeled through a spike-and-slab mixture at each location-scale combination along with a normal-inverse-Gamma (NIG) conjugate setup for the coefficients and errors. A graphical model called the Markov grove (MG) is designed to jointly model the spike-and-slab statuses at all location-scale combinations, which incorporates the clustering of each factor effect in the wavelet-domain thereby allowing borrowing of strength across location and scale. The posterior of this NIG-MG model is analytically available through a pyramid algorithm of the same computational complexity as Mallat's pyramid algorithm for discrete wavelet transform, i.e., linear in both the number of observations and the number of locations. Posterior probabilities of factor contributions can also be computed through pyramid recursion, and exact samples from the posterior can be drawn without MCMC. We investigate the performance of our method through extensive simulation and show that it outperforms existing wavelet-domain fANOVA methods in a variety of common settings. We apply the method to analyzing the orthosis data.

We propose the segmented iHMM (siHMM), a hierarchical infinite hidden Markov model (iHMM) that supports a simple, efficient inference scheme. The siHMM is well suited to segmentation problems, where the goal is to identify points at which a time series transitions from one relatively stable regime to a new regime. Conventional iHMMs often struggle with such problems, since they have no mechanism for distinguishing between high- and low-level dynamics. Hierarchical HMMs (HHMMs) can do better, but they require much more complex and expensive inference algorithms. The siHMM retains the simplicity and efficiency of the iHMM, but outperforms it on a variety of segmentation problems, achieving performance that matches or exceeds that of a more complicated HHMM.

Which song will Smith listen to next? Which restaurant will Alice go to tomorrow? Which product will John click next? These applications have in common the prediction of user trajectories that are in a constant state of flux over a hidden network (e.g. website links, geographic location). What users are doing now may be unrelated to what they will be doing in an hour from now. Mindful of these challenges we propose TribeFlow, a method designed to cope with the complex challenges of learning personalized predictive models of non-stationary, transient, and time-heterogeneous user trajectories. TribeFlow is a general method that can perform next product recommendation, next song recommendation, next location prediction, and general arbitrary-length user trajectory prediction without domain-specific knowledge. TribeFlow is more accurate and up to 413x faster than top competitors.

We present a supervised neural network model for polyphonic piano music transcription. The architecture of the proposed model is analogous to speech recognition systems and comprises an acoustic model and a music language model. The acoustic model is a neural network used for estimating the probabilities of pitches in a frame of audio. The language model is a recurrent neural network that models the correlations between pitch combinations over time. The proposed model is general and can be used to transcribe polyphonic music without imposing any constraints on the polyphony. The acoustic and language model predictions are combined using a probabilistic graphical model. Inference over the output variables is performed using the beam search algorithm. We perform two sets of experiments. We investigate various neural network architectures for the acoustic models and also investigate the effect of combining acoustic and music language model predictions using the proposed architecture. We compare performance of the neural network based acoustic models with two popular unsupervised acoustic models. Results show that convolutional neural network acoustic models yields the best performance across all evaluation metrics. We also observe improved performance with the application of the music language models. Finally, we present an efficient variant of beam search that improves performance and reduces run-times by an order of magnitude, making the model suitable for real-time applications.

We present a Hidden Markov Model-based algorithm for constructing timescales for paleoclimate records by annual layer counting. This objective, statistics-based approach has a number of major advantages over the current manual approach, beginning with speed. Manual layer counting of a single core (up to 3km in length) can require multiple person-years of time; the StratiCounter algorithm can count up to 100 layers/min, corresponding to a full-length timescale constructed in a few days. Moreover, the algorithm gives rigorous uncertainty estimates for the resulting timescale, which are far smaller than those produced manually. We demonstrate the utility of StratiCounter by applying it to ice-core data from two cores from Greenland and Antarctica. Performance of the algorithm is comparable to a manual approach. When using all available data, false-discovery rates and miss rates are 1-1.2% and 1.2-1.6%, respectively, for the two cores. For one core, even better agreement is found when using only the chemistry series primarily employed by human experts in the manual approach.

Loss of Control (LOC) is the most common precursor to aircraft accidents. This paper presents a Flight Safety Assessment and Management (FSAM) decision system to reduce in-flight LOC risk. FSAM nominally serves as a monitor to detect conditions that pose LOC risk, automatically activating the appropriate control authority if necessary to prevent LOC and restore a safe operational state. This paper contributes an efficient Markov Decision Process (MDP) formulation for FSAM. The state features capture risk associated with aircraft dynamics, configuration, health, pilot behavior and weather. The reward function trades cost of inaction against the cost of overriding the current control authority. A sparse sampling algorithm obtains a near-optimal solution for the MDP online. This approach enables the FSAM MDP to incorporate dynamically changing flight envelope and environment constraints into decision-making. Case studies based on real-world aviation incidents are presented.

Given a Markov Decision Process (MDP) with $n$ states and a totalnumber $m$ of actions, we study the number of iterations needed byPolicy Iteration (PI) algorithms to converge to the optimal$\gamma$-discounted policy. We consider two variations of PI: Howard'sPI that changes the actions in all states with a positive advantage,and Simplex-PI that only changes the action in the state with maximaladvantage. We show that Howard's PI terminates after at most $O\left(\frac{m}{1-\gamma}\log\left(\frac{1}{1-\gamma}\right)\right)$iterations, improving by a factor $O(\log n)$ a result by Hansen etal., while Simplex-PI terminates after at most $O\left(\frac{nm}{1-\gamma}\log\left(\frac{1}{1-\gamma}\right)\right)$iterations, improving by a factor $O(\log n)$ a result by Ye. Undersome structural properties of the MDP, we then consider bounds thatare independent of the discount factor~$\gamma$: quantities ofinterest are bounds $\tau\_t$ and $\tau\_r$---uniform on all states andpolicies---respectively on the \emph{expected time spent in transientstates} and \emph{the inverse of the frequency of visits in recurrentstates} given that the process starts from the uniform distribution.Indeed, we show that Simplex-PI terminates after at most $\tilde O\left(n^3 m^2 \tau\_t \tau\_r \right)$ iterations. This extends arecent result for deterministic MDPs by Post & Ye, in which $\tau\_t\le 1$ and $\tau\_r \le n$, in particular it shows that Simplex-PI isstrongly polynomial for a much larger class of MDPs. We explain whysimilar results seem hard to derive for Howard's PI. Finally, underthe additional (restrictive) assumption that the state space ispartitioned in two sets, respectively states that are transient andrecurrent for all policies, we show that both Howard's PI andSimplex-PI terminate after at most $\tilde O(m(n^2\tau\_t+n\tau\_r))$iterations.

We present a data-efficient reinforcement learning algorithm resistant to observation noise. Our method extends the highly data-efficient PILCO algorithm (Deisenroth & Rasmussen, 2011) into partially observed Markov decision processes (POMDPs) by considering the filtering process during policy evaluation. PILCO conducts policy search, evaluating each policy by first predicting an analytic distribution of possible system trajectories. We additionally predict trajectories w.r.t. a filtering process, achieving significantly higher performance than combining a filter with a policy optimised by the original (unfiltered) framework. Our test setup is the cartpole swing-up task with sensor noise, which involves nonlinear dynamics and requires nonlinear control.

Recommender systems play a central role in providing individualized access to information and services. This paper focuses on collaborative filtering, an approach that exploits the shared structure among mind-liked users and similar items. In particular, we focus on a formal probabilistic framework known as Markov random fields (MRF). We address the open problem of structure learning and introduce a sparsity-inducing algorithm to automatically estimate the interaction structures between users and between items. Item-item and user-user correlation networks are obtained as a by-product. Large-scale experiments on movie recommendation and date matching datasets demonstrate the power of the proposed method.