We propose a machine learning based framework for building a hierarchical monitoring system to detect and diagnose service issues. We demonstrate its use for building a monitoring system for a distributed data storage and computing service consisting of tens of thousands of machines. Our solution has been deployed in production as an end-to-end system, starting from telemetry data collection from individual machines, to a visualization tool for service operators to examine the detection outputs. Evaluation results are presented on detecting 19 customer impacting issues in the past three months.

Categories in multi-class data are often part of an underlying semantic taxonomy. Recent work in object classification has found interesting ways to use this taxonomy structure to develop better recognition algorithms. Here we propose a novel framework to learn similarity metrics using the class taxonomy. We show that a nearest neighbor classifier using the learned metrics gets improved performance over the best discriminative methods. Moreover, by incorporating the taxonomy, our learned metrics can also help in some taxonomy specific applications. We show that the metrics can help determine the correct placement of a new category that was not part of the original taxonomy, and can provide effective classification amongst categories local to specific subtrees of the taxonomy.

Fast nearest neighbor search is necessary for a variety of large scale web applications such as information retrieval, nearest neighbor classification and nearest neighbor regression. Recently a number of machine learning algorithms have been proposed for representing the data to be searched as (short) bit vectors and then using hashing to do rapid search. These algorithms have been limited in their applicability in that they are suited for only one type of task -- e.g. Spectral Hashing learns bit vector representations for retrieval, but not say, classification. In this paper we present a unified approach to learning bit vector representations for many applications that use nearest neighbor search. The main contribution is a single learning algorithm that can be customized to learn a bit vector representation suited for the task at hand. This broadens the usefulness of bit vector representations to tasks beyond just conventional retrieval. We propose a learning-to-rank formulation to learn the bit vector representation of the data. LambdaRank algorithm is used for learning a function that computes a task-specific bit vector from an input data vector. Our approach outperforms state-of-the-art nearest neighbor methods on a number of real world text and image classification and retrieval datasets. It is scalable and learns a 32-bit representation on 1.46 million training cases in two days.

We present a new approach to learning attribute-based descriptions of objects. Unlike earlier works, we do not assume that the descriptions are hand-labeled. Instead, our approach jointly learns both the attribute classifiers and the descriptions from data. By incorporating class information into the attribute classifier learning, we get an attribute-level representation that generalizes well to both unseen examples of known classes and unseen classes. We consider two different settings, one with unlabeled images available for learning, and another without. The former corresponds to a novel transductive setting where the unlabeled images can come from new classes. Results from Animals with Attributes and a-Yahoo, a-Pascal benchmark datasets show that the learned representations give similar or even better accuracy than the hand-labeled descriptions.

We introduce a new type of Deep Belief Net and evaluate it on a 3D object recognition task. The top-level model is a third-order Boltzmann machine, trained using a hybrid algorithm that combines both generative and discriminative gradients. Performance is evaluated on the NORB database(normalized-uniform version), which contains stereo-pair images of objects under different lighting conditions and viewpoints. Our model achieves 6.5% error on the test set, which is close to the best published result for NORB (5.9%) using a convolutional neural net that has built-in knowledge of translation invariance. It substantially outperforms shallow models such as SVMs (11.6%). DBNs are especially suited for semi-supervised learning, and to demonstrate this we consider a modified version of the NORB recognition task in which additional unlabeled images are created by applying small translations to the images in the database. With the extra unlabeled data (and the same amount of labeled data as before), our model achieves 5.2% error, making it the current best result for NORB.

We present a mixture model whose components are Restricted Boltzmann Machines (RBMs). This possibility has not been considered before because computing the partition function of an RBM is intractable, which appears to make learning a mixture of RBMs intractable as well. Surprisingly, when formulated as a third-order Boltzmann machine, such a mixture model can be learned tractably using contrastive divergence. The energy function of the model captures three-way interactions among visible units, hidden units, and a single hidden multinomial unit that represents the cluster labels. The distinguishing feature of this model is that, unlike other mixture models, the mixing proportions are not explicitly parameterized. Instead, they are defined implicitly via the energy function and depend on all the parameters in the model. We present results for the MNIST and NORB datasets showing that the implicit mixture of RBMs learns clusters that reflect the class structure in the data.

We describe a generative model for handwritten digits that uses two pairs of opposing springs whose stiffnesses are controlled by a motor program. We show how neural networks can be trained to infer the motor programs required to accurately reconstruct the MNIST digits. The inferred motor programs can be used directly for digit classification, but they can also be used in other ways. By adding noise to the motor program inferred from an MNIST image we can generate a large set of very different images of the same class, thus enlarging the training set available to other methods. We can also use the motor programs as additional, highly informative outputs which reduce overfitting when training a feed-forward classifier. 1 Overview The idea that patterns can be recognized by figuring out how they were generated has been around for at least half a century [1, 2] and one of the first proposed applications was the recognition of handwriting using a generative model that involved pairs of opposing springs [3, 4]. The “analysis-by-synthesis” approach is attractive because the true generative model should provide the most natural way to characterize a class of patterns. The handwritten 2’s in figure 1, for example, are very variable when viewed as pixels but they have very similar motor programs. Despite its obvious merits, analysis-by-synthesis has had few successes, partly because it is computationally expensive to invert non-linear generative models and partly because the underlying parameters of the generative model are unknown for most large data sets. For example, the only source of information about how the MNIST digits were drawn is the images themselves. We describe a simple generative model in which a pen is controlled by two pairs of op- posing springs whose stiffnesses are specified by a motor program. If the sequence of stiffnesses is specified correctly, the model can produce images which look very like the MNIST digits. Using a separate network for each digit class, we show that backpropaga- tion can be used to learn a “recognition” network that maps images to the motor programs required to produce them. An interesting aspect of this learning is that the network creates its own training data, so it does not require the training images to be labelled with motor programs. Each recognition network starts with a single example of a motor program and grows an “island of competence” around this example, progressively extending the region over which it can map small changes in the image to the corresponding small changes in the motor program (see figure 2). Figure 1: An MNIST image of a 2 and the additional images that can be generated by infer- ring the motor program and then adding random noise to it. The pixels are very different, but they are all clearly twos. Fairly good digit recognition can be achieved by using the 10 recognition networks to find 10 motor programs for a test image and then scoring each motor program by its squared error in reconstructing the image. The 10 scores are then fed into a softmax classifier. Recognition can be improved by using PCA to model the distribution of motor trajectories for each class and using the distance of a motor trajectory from the relevant PCA hyperplane as an additional score. Each recognition network is solving a difficult global search problem in which the correct motor program must be found by a single, “open-loop” pass through the network. More accurate recognition can be achieved by using this open-loop global search to initialize an iterative, closed-loop local search which uses the error in the reconstructed image to re- vise the motor program. This requires reconstruction errors in pixel space to be mapped to corrections in the space of spring stiffnesses. We cannot backpropagate errors through the generative model because it is just a hand-coded computer program. So we learn “genera- tive” networks, one per digit class, that emulate the generator. After learning, backpropa- gation through these generative networks is used to convert pixel reconstruction errors into stiffness corrections. Our final system gives 1.82% error on the MNIST test set which is similar to the 1.7% achieved by a very different generative approach [5] but worse than the 1.53% produced by the best backpropagation networks or the 1.4% produced by support vector machines [6]. It is much worse than the 0.4% produced by convolutional neural networks that use cleverly enhanced training sets [7]. Recognition of test images is quite slow because it uses ten different recognition networks followed by iterative local search. There is, however, a much more efficient way to make use of our ability to extract motor programs. They can be treated as additional output labels when using backpropagation to train a single, multi- layer, discriminative neural network. These additional labels act as a very informative regularizer that reduces the error rate from 1.53% to 1.27% in a network with two hidden layers of 500 units each. This is a new method of improving performance that can be used in conjunction with other tricks such as preprocessing the images, enhancing the training set or using convolutional neural nets [8, 7]. 2 A simple generative model for drawing digits The generative model uses two pairs of opposing springs at right angles. One end of each spring is attached to a frictionless horizontal or vertical rail that is 39 pixels from the center of the image. The other end is attached to a “pen” that has significant mass. The springs themselves are weightless and have zero rest length. The pen starts at the equilibrium position defined by the initial stiffnesses of the four springs. It then follows a trajectory that is determined by the stiffness of each spring at each of the 16 subsequent time steps in the motor program. The mass is large compared with the rate at which the stiffnesses change, so the system is typically far from equilibrium as it follows the smooth trajectory. On each time step, the momentum is multiplied by 0.9 to simulate viscosity. A coarse-grain trajectory is computed by using one step of forward integration for each time step in the motor program, so it contains 17 points. The code is at www.cs.toronto.edu/∼ hinton/code. Figure 2: The training data for each class-specific recognition network is produced by adding noise to motor programs that are inferred from MNIST images using the current parameters of the recognition network. To initiate this process, the biases of the output units are set by hand so that they represent a prototypical motor program for the class. Given a coarse-grain trajectory, we need a way of assigning an intensity to each pixel. We tried various methods until we hand-evolved one that was able to reproduce the MNIST im- ages fairly accurately, but we suspect that many other methods would be just as good. For each point on the coarse trajectory, we share two units of ink between the the four closest pixels using bilinear interpolation. We also use linear interpolation to add three fine-grain trajectory points between every pair of coarse-grain points. These fine-grain points also contribute ink to the pixels using bilinear interpolation, but the amount of ink they con- tribute is zero if they are less than one pixel apart and rises linearly to the same amount as the coarse-grain points if they are more than two pixels apart. This generates a thin skeleton with a fairly uniform ink density. To flesh-out the skeleton, we use two “ink parameters”, a, b, to specify a 3 × 3 kernel of the form b(1 + a)[ a 12 ] which is convolved with the image four times. Finally, the pixel intensities are clipped to lie in the interval [0,1]. The matlab code is at www.cs.toronto.edu/∼ hinton/code. The values of 2a and b/1.5 are additional, logistic outputs of the recognition networks1.