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This paper investigates different methods and various neural network architectures applicable in the time series classification domain. The data is obtained from a fleet of gas sensors that measure and track quantities such as oxygen and sound. With the help of this data, we can detect events such as occupancy in a specific environment. At first, we analyze the time series data to understand the effect of different parameters, such as the sequence length, when training our models. These models employ Fully Convolutional Networks (FCN) and Long Short-Term Memory (LSTM) for supervised learning and Recurrent Autoencoders for semisupervised learning. Throughout this study, we spot the differences between these methods based on metrics such as precision and recall identifying which technique best suits this problem.

The paradigm of self-supervision focuses on representation learning from raw data without the need of labor-consuming annotations, which is the main bottleneck of current data-driven methods. Self-supervision tasks are often used to pre-train a neural network with a large amount of unlabeled data and extract generic features of the dataset. The learned model is likely to contain useful information which can be transferred to the downstream main task and improve performance compared to random parameter initialization. In this paper, we propose a new self-supervision task called source identification (SI), which is inspired by the classic blind source separation problem. Synthetic images are generated by fusing multiple source images and the network's task is to reconstruct the original images, given the fused images. A proper understanding of the image content is required to successfully solve the task. We validate our method on two medical image segmentation tasks: brain tumor segmentation and white matter hyperintensities segmentation. The results show that the proposed SI task outperforms traditional self-supervision tasks for dense predictions including inpainting, pixel shuffling, intensity shift, and super-resolution. Among variations of the SI task fusing images of different types, fusing images from different patients performs best.

Supervised learning typically focuses on learning transferable representations from training examples annotated by humans. While rich annotations (like soft labels) carry more information than sparse annotations (like hard labels), they are also more expensive to collect. For example, while hard labels only provide information about the closest class an object belongs to (e.g., "this is a dog"), soft labels provide information about the object's relationship with multiple classes (e.g., "this is most likely a dog, but it could also be a wolf or a coyote"). We use information theory to compare how a number of commonly-used supervision signals contribute to representation-learning performance, as well as how their capacity is affected by factors such as the number of labels, classes, dimensions, and noise. Our framework provides theoretical justification for using hard labels in the big-data regime, but richer supervision signals for few-shot learning and out-of-distribution generalization. We validate these results empirically in a series of experiments with over 1 million crowdsourced image annotations and conduct a cost-benefit analysis to establish a tradeoff curve that enables users to optimize the cost of supervising representation learning on their own datasets.

Probability density estimation is a core problem of statistics and signal processing. Moment methods are an important means of density estimation, but they are generally strongly dependent on the choice of feasible functions, which severely affects the performance. In this paper, we propose a non-classical parametrization for density estimation using sample moments, which does not require the choice of such functions. The parametrization is induced by the squared Hellinger distance, and the solution of it, which is proved to exist and be unique subject to a simple prior that does not depend on data, and can be obtained by convex optimization. Statistical properties of the density estimator, together with an asymptotic error upper bound are proposed for the estimator by power moments. Applications of the proposed density estimator in signal processing tasks are given. Simulation results validate the performance of the estimator by a comparison to several prevailing methods. To the best of our knowledge, the proposed estimator is the first one in the literature for which the power moments up to an arbitrary even order exactly match the sample moments, while the true density is not assumed to fall within specific function classes.

We consider a model identification problem in which an outcome variable contains nonignorable missing values. Statistical inference requires a guarantee of the model identifiability to obtain estimators enjoying theoretically reasonable properties such as consistency and asymptotic normality. Recently, instrumental or shadow variables, combined with the completeness condition in the outcome model, have been highlighted to make a model identifiable. However, the completeness condition may not hold even for simple models when the instrument is categorical. We propose a sufficient condition for model identifiability, which is applicable to cases where establishing the completeness condition is difficult. Using observed data, we demonstrate that the proposed conditions are easy to check for many practical models and outline their usefulness in numerical experiments and real data analysis.

One of the most important hyper-parameters in duration-dependent Markov-switching (DDMS) models is the duration of the hidden states. Because there is currently no procedure for estimating this duration or testing whether a given duration is appropriate for a given data set, an ad hoc duration choice must be heuristically justified. This is typically a difficult task and is likely the most delicate point of the modeling procedure, allowing for criticism and ultimately hindering the use of DDMS models. In this paper, we propose and examine a methodology that mitigates the choice of duration in DDMS models when forecasting is the goal. The idea is to use a parametric link instead of the usual fixed link when calculating transition probabilities. As a result, the model becomes more flexible and any potentially incorrect duration choice (i.e., misspecification) is compensated by the parameter in the link, yielding a likelihood and transition probabilities very close to the true ones while, at the same time, improving forecasting accuracy under misspecification. We evaluate the proposed approach in Monte Carlo simulations and using real data applications. Results indicate that the parametric link model outperforms the benchmark logit model, both in terms of in-sample estimation and out-of-sample forecasting, for both well-specified and misspecified duration values.

The volume function V(t) of a compact set S\in R^d is just the Lebesgue measure of the set of points within a distance to S not larger than t. According to some classical results in geometric measure theory, the volume function turns out to be a polynomial, at least in a finite interval, under a quite intuitive, easy to interpret, sufficient condition (called ``positive reach'') which can be seen as an extension of the notion of convexity. However, many other simple sets, not fulfilling the positive reach condition, have also a polynomial volume function. To our knowledge, there is no general, simple geometric description of such sets. Still, the polynomial character of $V(t)$ has some relevant consequences since the polynomial coefficients carry some useful geometric information. In particular, the constant term is the volume of S and the first order coefficient is the boundary measure (in Minkowski's sense). This paper is focused on sets whose volume function is polynomial on some interval starting at zero, whose length (that we call ``polynomial reach'') might be unknown. Our main goal is to approximate such polynomial reach by statistical means, using only a large enough random sample of points inside S. The practical motivation is simple: when the value of the polynomial reach , or rather a lower bound for it, is approximately known, the polynomial coefficients can be estimated from the sample points by using standard methods in polynomial approximation. As a result, we get a quite general method to estimate the volume and boundary measure of the set, relying only on an inner sample of points and not requiring the use any smoothing parameter. This paper explores the theoretical and practical aspects of this idea.

Many tasks in natural language processing can be viewed as multi-label classification problems. However, most of the existing models are trained with the standard cross-entropy loss function and use a fixed prediction policy (e.g., a threshold of 0.5) for all the labels, which completely ignores the complexity and dependencies among different labels. In this paper, we propose a meta-learning method to capture these complex label dependencies. More specifically, our method utilizes a meta-learner to jointly learn the training policies and prediction policies for different labels. The training policies are then used to train the classifier with the cross-entropy loss function, and the prediction policies are further implemented for prediction. Experimental results on fine-grained entity typing and text classification demonstrate that our proposed method can obtain more accurate multi-label classification results.

With the rapid increase of large-scale, real-world datasets, it becomes critical to address the problem of long-tailed data distribution (i.e., a few classes account for most of the data, while most classes are under-represented). Existing solutions typically adopt class re-balancing strategies such as re-sampling and re-weighting based on the number of observations for each class. In this work, we argue that as the number of samples increases, the additional benefit of a newly added data point will diminish. We introduce a novel theoretical framework to measure data overlap by associating with each sample a small neighboring region rather than a single point. The effective number of samples is defined as the volume of samples and can be calculated by a simple formula $(1-\beta^{n})/(1-\beta)$, where $n$ is the number of samples and $\beta \in [0,1)$ is a hyperparameter. We design a re-weighting scheme that uses the effective number of samples for each class to re-balance the loss, thereby yielding a class-balanced loss. Comprehensive experiments are conducted on artificially induced long-tailed CIFAR datasets and large-scale datasets including ImageNet and iNaturalist. Our results show that when trained with the proposed class-balanced loss, the network is able to achieve significant performance gains on long-tailed datasets.

High spectral dimensionality and the shortage of annotations make hyperspectral image (HSI) classification a challenging problem. Recent studies suggest that convolutional neural networks can learn discriminative spatial features, which play a paramount role in HSI interpretation. However, most of these methods ignore the distinctive spectral-spatial characteristic of hyperspectral data. In addition, a large amount of unlabeled data remains an unexploited gold mine for efficient data use. Therefore, we proposed an integration of generative adversarial networks (GANs) and probabilistic graphical models for HSI classification. Specifically, we used a spectral-spatial generator and a discriminator to identify land cover categories of hyperspectral cubes. Moreover, to take advantage of a large amount of unlabeled data, we adopted a conditional random field to refine the preliminary classification results generated by GANs. Experimental results obtained using two commonly studied datasets demonstrate that the proposed framework achieved encouraging classification accuracy using a small number of data for training.