Researchers are often faced with the challenge of developing statistical models with incomplete data. Exacerbating this situation is the possibility that either the researcher's complete-data model or the model of the missing-data mechanism is misspecified. In this article, we create a formal theoretical framework for developing statistical models and detecting model misspecification in the presence of incomplete data where maximum likelihood estimates are obtained by maximizing the observable-data likelihood function when the missing-data mechanism is assumed ignorable. First, we provide sufficient regularity conditions on the researcher's complete-data model to characterize the asymptotic behavior of maximum likelihood estimates in the simultaneous presence of both missing data and model misspecification. These results are then used to derive robust hypothesis testing methods for possibly misspecified models in the presence of Missing at Random (MAR) or Missing Not at Random (MNAR) missing data.

Bayes' Theorem is something that confuses and frustrates many, but is not as awful as many make it out to be. While the formula for "Bae's Theorem" given in the graphic above is silly, doesn't make mathematical sense, and borders on being NSFW, it does help illustrate what the problem statement is (something that throws many, as intuitively it seems kind of backwards). Given that Netflix is occurring, one would want to know the probability of'chill', NOT the other way around. Granted, the right side of the equation is complete nonsense, but the left-side is actually a good mnemonic device, especially given that part of the reason so many students tune-out while learning mathematics is due to the dry sterility of the presentation. The theorem essentially states that: the probability of event A given event B is equal to the probability of B given event A times the probability of event A divided by the probability of B. Which seems very complex without breaking it down bit by bit.

In this paper, we aimed at reviewing present literature on employing nonlinear analysis in combination with machine learning methods, in depression detection or prediction task. We are focusing on an affordable data-driven approach, applicable for everyday clinical practice, and in particular, those based on electroencephalographic (EEG) recordings. Among those studies utilizing EEG, we are discussing a group of applications used for detecting the depression based on the resting state EEG (detection studies) and interventional studies (using stimulus in their protocols or aiming to predict the outcome of therapy). We conclude with a discussion and review of guidelines to improve the reliability of developed models that could serve the improvement of diagnostic and more accurate treatment of depression.

We present a system that automatically discovers critical mechanics in a variety of video games within the General Video Game Artificial Intelligence (GVG-AI) framework using a combination of game description parsing and playtrace information. Critical mechanics are defined as the mechanics most necessary to trigger in order to perform well in the game. In a user study, human-identified mechanics are compared against system-identified mechanics to verify alignment between humans and the system. The results of the study demonstrate that our method is able to match humans with high consistency. Our system is further validated by comparing MCTS agents augmented with critical mechanic information against baseline MCTS agents on 4 games in GVG-AI. The augmented agents show a significant performance improvement over their baseline counterparts for all 4 tested games, demonstrating that knowledge of system-identified mechanics are responsible for improved performance.

This framework has been shown to substantially reduce data needs by leveraging domain-independent dimensions, such as social obligations or feedback, which (as we show) can be transferred between domains. In this paper, we conduct a user study and show that the performance of a multidimensional system, which can be adapted from a source domain, is equivalent to that of a one-dimensional baseline, which can only be trained from scratch. 1 Introduction Data-driven approaches to spoken dialogue systems (SDS) are limited by their reliance on substantial amounts of annotated data in the target domain. This can be addressed by considering transfer learning techniques, e.g.

The majority of multi-agent system (MAS) implementations aim to optimise agents' policies with respect to a single objective, despite the fact that many real-world problem domains are inherently multi-objective in nature. Multi-objective multi-agent systems (MOMAS) explicitly consider the possible trade-offs between conflicting objective functions. We argue that, in MOMAS, such compromises should be analysed on the basis of the utility that these compromises have for the users of a system. As is standard in multi-objective optimisation, we model the user utility using utility functions that map value or return vectors to scalar values. This approach naturally leads to two different optimisation criteria: expected scalarised returns (ESR) and scalarised expected returns (SER). We develop a new taxonomy which classifies multi-objective multi-agent decision making settings, on the basis of the reward structures, and which and how utility functions are applied. This allows us to offer a structured view of the field, to clearly delineate the current state-of-the-art in multi-objective multi-agent decision making approaches and to identify promising directions for future research. Starting from the execution phase, in which the selected policies are applied and the utility for the users is attained, we analyse which solution concepts apply to the different settings in our taxonomy. Furthermore, we define and discuss these solution concepts under both ESR and SER optimisation criteria. We conclude with a summary of our main findings and a discussion of many promising future research directions in multi-objective multi-agent systems.

A hierarchical Bayesian classifier is trained at pixel scale with spectral data from the CRISM (Compact Reconnaissance Imaging Spectrometer for Mars) imagery. Its utility in detecting rare phases is demonstrated with new geologic discoveries near the Mars-2020 rover landing site. Akaganeite is found in sediments on the Jezero crater floor and in fluvial deposits at NE Syrtis. Jarosite and silica are found on the Jezero crater floor while chlorite-smectite and Al phyllosilicates are found in the Jezero crater walls. These detections point to a multi-stage, multi-chemistry history of water in Jezero crater and the surrounding region and provide new information for guiding the Mars-2020 rover's landed exploration. In particular, the akaganeite, silica, and jarosite in the floor deposits suggest either a later episode of salty, Fe-rich waters that post-date Jezero delta or groundwater alteration of portions of the Jezero sedimentary sequence.

Radio tomographic imaging (RTI) is an emerging technology for localization of physical objects in a geographical area covered by wireless networks. With attenuation measurements collected at spatially distributed sensors, RTI capitalizes on spatial loss fields (SLFs) measuring the absorption of radio frequency waves at spatial locations along the propagation path. These SLFs can be utilized for interference management in wireless communication networks, environmental monitoring, and survivor localization after natural disasters such as earthquakes. Key to the success of RTI is to accurately model shadowing as the weighted line integral of the SLF. To learn the SLF exhibiting statistical heterogeneity induced by spatially diverse environments, the present work develops a Bayesian framework entailing a piecewise homogeneous SLF with an underlying hidden Markov random field model. Utilizing variational Bayes techniques, the novel approach yields efficient field estimators at affordable complexity. A data-adaptive sensor selection strategy is also introduced to collect informative measurements for effective reconstruction of the SLF. Numerical tests using synthetic and real datasets demonstrate the capabilities of the proposed approach to radio tomography and channel-gain estimation.

--Shallow water environments create a challenging channel for communications. In this paper, we focus on the challenges posed by the frequency-selective signal distortion called the Doppler effect. We explore the design and performance of machine learning (ML) based demodulation methods -- (1) Deep Belief Network-feed forward Neural Network (DBN-NN) and (2) Deep Belief Network-Convolutional Neural Network (DBN-CNN) in the physical layer of Shallow Water Acoustic Communication (SW AC). The proposed method comprises of a ML based feature extraction method and classification technique. First, the feature extraction converts the received signals to feature images. An analysis of the ML based proposed demodulation shows that despite the presence of instantaneous frequencies, the performance of the algorithm shows an invariance with a small 2dB error margin in terms of bit error rate (BER).

Neural currents in the brain can be estimated from MEG/EEG recordings by solving the inverse problem (Hamalainen et al. 1993; Mosher, Leahy, and Lewis 1999) . The inverse problem is ill - posed: several current distributions can produce the same or similar electric and magnetic fields outside the head and the e stimates therefore become sensitive to measurement noise (Hamalainen et al. 1993; Helmholtz 1853) . These difficulties limit the spatial resolution and reliability of neural current estimates derived from MEG/EEG signals. To deal with this ill - posedness of the inve rse problem, constraints limiting the space of possible neural current configurations and regularization are often used. Solving the inverse problem requires a forward model that calculates the MEG/EEG signals from given current distributions in the brain (Sarvas 1987; Mosher, Leahy, and Lewis 1999; Stenroos, Hunold, and Haueisen 2014) . Popular methods for solving the inverse problem include discrete current dipole models (Schneider 1972; Scherg and Cramon 1985; Moshe r, Lewis, and Leahy 1992; Leahy et al. 1998) as well as distributed current models (Hamalainen and Ilmoniemi 1994; Uutela, Hamalainen, and Somersalo 1999; Baillet, Mosher, and Leahy 2001; Stenbacka et al. 2002) . Importantly, most source estimation methods are derived sample by sample, i.e., without assuming any relationship between the current distributions across time.