Anand Ramakrishnan

Anand Ramakrishnan, Minh Pham, Jacob Whitehill

For the task of face verification, we explore the utility of harnessing auxiliary facial emotion labels to impose explicit geometric constraints on the embedding space when training deep embedding models. We introduce several novel loss functions that, in conjunction with a standard Triplet Loss [43], or ArcFace loss [10], provide geometric constraints on the embedding space; the labels for our loss functions can be provided using either manually annotated or automatically detected auxiliary emotion labels. Our method is implemented purely in terms of the loss function and does not require any changes to the neural network backbone of the embedding function.

Anand Ramakrishnan, Warren B. Jackson, Kent Evans

Deep learning models are trained to minimize the error between the model's output and the actual values. The typical cost function, the Mean Squared Error (MSE), arises from maximizing the log-likelihood of additive independent, identically distributed Gaussian noise. However, minimizing MSE fails to minimize the residuals' cross-correlations, leading to over-fitting and poor extrapolation of the model outside the training set (generalization). In this paper, we introduce a "whitening" cost function, the Ljung-Box statistic, which not only minimizes the error but also minimizes the correlations between errors, ensuring that the fits enforce compatibility with an independent and identically distributed (i.i.d) gaussian noise model. The results show significant improvement in generalization for recurrent neural networks (RNNs) (1d) and image autoencoders (2d). Specifically, we look at both temporal correlations for system-id in simulated and actual mechanical systems. We also look at spatial correlation in vision autoencoders to demonstrate that the whitening objective functions lead to much better extrapolation--a property very desirable for reliable control systems.

Jacob Whitehill, Anand Ramakrishnan

Automatic machine learning-based detectors of various psychological and social phenomena (e.g., emotion, stress, engagement) have great potential to advance basic science. However, when a detector $d$ is trained to approximate an existing measurement tool (e.g., a questionnaire, observation protocol), then care must be taken when interpreting measurements collected using $d$ since they are one step further removed from the underlying construct. We examine how the accuracy of $d$, as quantified by the correlation $q$ of $d$'s outputs with the ground-truth construct $U$, impacts the estimated correlation between $U$ (e.g., stress) and some other phenomenon $V$ (e.g., academic performance). In particular: (1) We show that if the true correlation between $U$ and $V$ is $r$, then the expected sample correlation, over all vectors $\mathcal{T}^n$ whose correlation with $U$ is $q$, is $qr$. (2) We derive a formula for the probability that the sample correlation (over $n$ subjects) using $d$ is positive given that the true correlation is negative (and vice-versa); this probability can be substantial (around $20-30\%$) for values of $n$ and $q$ that have been used in recent affective computing studies. %We also show that this probability decreases monotonically in $n$ and in $q$. (3) With the goal to reduce the variance of correlations estimated by an automatic detector, we show that training multiple neural networks $d^{(1)},\ldots,d^{(m)}$ using different training architectures and hyperparameters for the same detection task provides only limited ``coverage'' of $\mathcal{T}^n$.