arXiv subjects

Anna Choromanska

Publications and source records attributed to Anna Choromanska.

51 records · Page 3Linked to original sources

arXiv2018

Invertible Autoencoder for domain adaptation

The unsupervised image-to-image translation aims at finding a mapping between the source ($A$) and target ($B$) image domains, where in many applications aligned image pairs are not available at training. This is an ill-posed learning problem since it requires inferring the joint probability distribution from marginals. Joint learning of coupled mappings $F_{AB}: A \rightarrow B$ and $F_{BA}: B \rightarrow A$ is commonly used by the state-of-the-art methods, like CycleGAN [Zhu et al., 2017], to learn this translation by introducing cycle consistency requirement to the learning problem, i.e. $F_{AB}(F_{BA}(B)) \approx B$ and $F_{BA}(F_{AB}(A)) \approx A$. Cycle consistency enforces the preservation of the mutual information between input and translated images. However, it does not explicitly enforce $F_{BA}$ to be an inverse operation to $F_{AB}$. We propose a new deep architecture that we call invertible autoencoder (InvAuto) to explicitly enforce this relation. This is done by forcing an encoder to be an inverted version of the decoder, where corresponding layers perform opposite mappings and share parameters. The mappings are constrained to be orthonormal. The resulting architecture leads to the reduction of the number of trainable parameters (up to $2$ times). We present image translation results on benchmark data sets and demonstrate state-of-the art performance of our approach. Finally, we test the proposed domain adaptation method on the task of road video conversion. We demonstrate that the videos converted with InvAuto have high quality and show that the NVIDIA neural-network-based end-to-end learning system for autonomous driving, known as PilotNet, trained on real road videos performs well when tested on the converted ones.

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arXiv2017

VisualBackProp: efficient visualization of CNNs

This paper proposes a new method, that we call VisualBackProp, for visualizing which sets of pixels of the input image contribute most to the predictions made by the convolutional neural network (CNN). The method heavily hinges on exploring the intuition that the feature maps contain less and less irrelevant information to the prediction decision when moving deeper into the network. The technique we propose was developed as a debugging tool for CNN-based systems for steering self-driving cars and is therefore required to run in real-time, i.e. it was designed to require less computations than a forward propagation. This makes the presented visualization method a valuable debugging tool which can be easily used during both training and inference. We furthermore justify our approach with theoretical arguments and theoretically confirm that the proposed method identifies sets of input pixels, rather than individual pixels, that collaboratively contribute to the prediction. Our theoretical findings stand in agreement with the experimental results. The empirical evaluation shows the plausibility of the proposed approach on the road video data as well as in other applications and reveals that it compares favorably to the layer-wise relevance propagation approach, i.e. it obtains similar visualization results and simultaneously achieves order of magnitude speed-ups.

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arXiv2017

Explaining How a Deep Neural Network Trained with End-to-End Learning Steers a Car

As part of a complete software stack for autonomous driving, NVIDIA has created a neural-network-based system, known as PilotNet, which outputs steering angles given images of the road ahead. PilotNet is trained using road images paired with the steering angles generated by a human driving a data-collection car. It derives the necessary domain knowledge by observing human drivers. This eliminates the need for human engineers to anticipate what is important in an image and foresee all the necessary rules for safe driving. Road tests demonstrated that PilotNet can successfully perform lane keeping in a wide variety of driving conditions, regardless of whether lane markings are present or not. The goal of the work described here is to explain what PilotNet learns and how it makes its decisions. To this end we developed a method for determining which elements in the road image most influence PilotNet's steering decision. Results show that PilotNet indeed learns to recognize relevant objects on the road. In addition to learning the obvious features such as lane markings, edges of roads, and other cars, PilotNet learns more subtle features that would be hard to anticipate and program by engineers, for example, bushes lining the edge of the road and atypical vehicle classes.

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arXiv2017

Entropy-SGD: Biasing Gradient Descent Into Wide Valleys

This paper proposes a new optimization algorithm called Entropy-SGD for training deep neural networks that is motivated by the local geometry of the energy landscape. Local extrema with low generalization error have a large proportion of almost-zero eigenvalues in the Hessian with very few positive or negative eigenvalues. We leverage upon this observation to construct a local-entropy-based objective function that favors well-generalizable solutions lying in large flat regions of the energy landscape, while avoiding poorly-generalizable solutions located in the sharp valleys. Conceptually, our algorithm resembles two nested loops of SGD where we use Langevin dynamics in the inner loop to compute the gradient of the local entropy before each update of the weights. We show that the new objective has a smoother energy landscape and show improved generalization over SGD using uniform stability, under certain assumptions. Our experiments on convolutional and recurrent networks demonstrate that Entropy-SGD compares favorably to state-of-the-art techniques in terms of generalization error and training time.

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arXiv2017

Simultaneous Learning of Trees and Representations for Extreme Classification and Density Estimation

We consider multi-class classification where the predictor has a hierarchical structure that allows for a very large number of labels both at train and test time. The predictive power of such models can heavily depend on the structure of the tree, and although past work showed how to learn the tree structure, it expected that the feature vectors remained static. We provide a novel algorithm to simultaneously perform representation learning for the input data and learning of the hierarchi- cal predictor. Our approach optimizes an objec- tive function which favors balanced and easily- separable multi-way node partitions. We theoret- ically analyze this objective, showing that it gives rise to a boosting style property and a bound on classification error. We next show how to extend the algorithm to conditional density estimation. We empirically validate both variants of the al- gorithm on text classification and language mod- eling, respectively, and show that they compare favorably to common baselines in terms of accu- racy and running time.

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arXiv2016

Structured adaptive and random spinners for fast machine learning computations

We consider an efficient computational framework for speeding up several machine learning algorithms with almost no loss of accuracy. The proposed framework relies on projections via structured matrices that we call Structured Spinners, which are formed as products of three structured matrix-blocks that incorporate rotations. The approach is highly generic, i.e. i) structured matrices under consideration can either be fully-randomized or learned, ii) our structured family contains as special cases all previously considered structured schemes, iii) the setting extends to the non-linear case where the projections are followed by non-linear functions, and iv) the method finds numerous applications including kernel approximations via random feature maps, dimensionality reduction algorithms, new fast cross-polytope LSH techniques, deep learning, convex optimization algorithms via Newton sketches, quantization with random projection trees, and more. The proposed framework comes with theoretical guarantees characterizing the capacity of the structured model in reference to its unstructured counterpart and is based on a general theoretical principle that we describe in the paper. As a consequence of our theoretical analysis, we provide the first theoretical guarantees for one of the most efficient existing LSH algorithms based on the HD3HD2HD1 structured matrix [Andoni et al., 2015]. The exhaustive experimental evaluation confirms the accuracy and efficiency of structured spinners for a variety of different applications.

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arXiv2016

Binary embeddings with structured hashed projections

We consider the hashing mechanism for constructing binary embeddings, that involves pseudo-random projections followed by nonlinear (sign function) mappings. The pseudo-random projection is described by a matrix, where not all entries are independent random variables but instead a fixed "budget of randomness" is distributed across the matrix. Such matrices can be efficiently stored in sub-quadratic or even linear space, provide reduction in randomness usage (i.e. number of required random values), and very often lead to computational speed ups. We prove several theoretical results showing that projections via various structured matrices followed by nonlinear mappings accurately preserve the angular distance between input high-dimensional vectors. To the best of our knowledge, these results are the first that give theoretical ground for the use of general structured matrices in the nonlinear setting. In particular, they generalize previous extensions of the Johnson-Lindenstrauss lemma and prove the plausibility of the approach that was so far only heuristically confirmed for some special structured matrices. Consequently, we show that many structured matrices can be used as an efficient information compression mechanism. Our findings build a better understanding of certain deep architectures, which contain randomly weighted and untrained layers, and yet achieve high performance on different learning tasks. We empirically verify our theoretical findings and show the dependence of learning via structured hashed projections on the performance of neural network as well as nearest neighbor classifier.

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arXiv2016

On the boosting ability of top-down decision tree learning algorithm for multiclass classification

We analyze the performance of the top-down multiclass classification algorithm for decision tree learning called LOMtree, recently proposed in the literature Choromanska and Langford (2014) for solving efficiently classification problems with very large number of classes. The algorithm online optimizes the objective function which simultaneously controls the depth of the tree and its statistical accuracy. We prove important properties of this objective and explore its connection to three well-known entropy-based decision tree objectives, i.e. Shannon entropy, Gini-entropy and its modified version, for which instead online optimization schemes were not yet developed. We show, via boosting-type guarantees, that maximizing the considered objective leads also to the reduction of all of these entropy-based objectives. The bounds we obtain critically depend on the strong-concavity properties of the entropy-based criteria, where the mildest dependence on the number of classes (only logarithmic) corresponds to the Shannon entropy.

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arXiv2015

Logarithmic Time Online Multiclass prediction

We study the problem of multiclass classification with an extremely large number of classes (k), with the goal of obtaining train and test time complexity logarithmic in the number of classes. We develop top-down tree construction approaches for constructing logarithmic depth trees. On the theoretical front, we formulate a new objective function, which is optimized at each node of the tree and creates dynamic partitions of the data which are both pure (in terms of class labels) and balanced. We demonstrate that under favorable conditions, we can construct logarithmic depth trees that have leaves with low label entropy. However, the objective function at the nodes is challenging to optimize computationally. We address the empirical problem with a new online decision tree construction procedure. Experiments demonstrate that this online algorithm quickly achieves improvement in test error compared to more common logarithmic training time approaches, which makes it a plausible method in computationally constrained large-k applications.

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arXiv2015

Deep learning with Elastic Averaging SGD

We study the problem of stochastic optimization for deep learning in the parallel computing environment under communication constraints. A new algorithm is proposed in this setting where the communication and coordination of work among concurrent processes (local workers), is based on an elastic force which links the parameters they compute with a center variable stored by the parameter server (master). The algorithm enables the local workers to perform more exploration, i.e. the algorithm allows the local variables to fluctuate further from the center variable by reducing the amount of communication between local workers and the master. We empirically demonstrate that in the deep learning setting, due to the existence of many local optima, allowing more exploration can lead to the improved performance. We propose synchronous and asynchronous variants of the new algorithm. We provide the stability analysis of the asynchronous variant in the round-robin scheme and compare it with the more common parallelized method ADMM. We show that the stability of EASGD is guaranteed when a simple stability condition is satisfied, which is not the case for ADMM. We additionally propose the momentum-based version of our algorithm that can be applied in both synchronous and asynchronous settings. Asynchronous variant of the algorithm is applied to train convolutional neural networks for image classification on the CIFAR and ImageNet datasets. Experiments demonstrate that the new algorithm accelerates the training of deep architectures compared to DOWNPOUR and other common baseline approaches and furthermore is very communication efficient.

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arXiv2015

Differentially- and non-differentially-private random decision trees

We consider supervised learning with random decision trees, where the tree construction is completely random. The method is popularly used and works well in practice despite the simplicity of the setting, but its statistical mechanism is not yet well-understood. In this paper we provide strong theoretical guarantees regarding learning with random decision trees. We analyze and compare three different variants of the algorithm that have minimal memory requirements: majority voting, threshold averaging and probabilistic averaging. The random structure of the tree enables us to adapt these methods to a differentially-private setting thus we also propose differentially-private versions of all three schemes. We give upper-bounds on the generalization error and mathematically explain how the accuracy depends on the number of random decision trees. Furthermore, we prove that only logarithmic (in the size of the dataset) number of independently selected random decision trees suffice to correctly classify most of the data, even when differential-privacy guarantees must be maintained. We empirically show that majority voting and threshold averaging give the best accuracy, also for conservative users requiring high privacy guarantees. Furthermore, we demonstrate that a simple majority voting rule is an especially good candidate for the differentially-private classifier since it is much less sensitive to the choice of forest parameters than other methods.

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arXiv2015

The Loss Surfaces of Multilayer Networks

We study the connection between the highly non-convex loss function of a simple model of the fully-connected feed-forward neural network and the Hamiltonian of the spherical spin-glass model under the assumptions of: i) variable independence, ii) redundancy in network parametrization, and iii) uniformity. These assumptions enable us to explain the complexity of the fully decoupled neural network through the prism of the results from random matrix theory. We show that for large-size decoupled networks the lowest critical values of the random loss function form a layered structure and they are located in a well-defined band lower-bounded by the global minimum. The number of local minima outside that band diminishes exponentially with the size of the network. We empirically verify that the mathematical model exhibits similar behavior as the computer simulations, despite the presence of high dependencies in real networks. We conjecture that both simulated annealing and SGD converge to the band of low critical points, and that all critical points found there are local minima of high quality measured by the test error. This emphasizes a major difference between large- and small-size networks where for the latter poor quality local minima have non-zero probability of being recovered. Finally, we prove that recovering the global minimum becomes harder as the network size increases and that it is in practice irrelevant as global minimum often leads to overfitting.

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arXiv2014

Notes on using Determinantal Point Processes for Clustering with Applications to Text Clustering

In this paper, we compare three initialization schemes for the KMEANS clustering algorithm: 1) random initialization (KMEANSRAND), 2) KMEANS++, and 3) KMEANSD++. Both KMEANSRAND and KMEANS++ have a major that the value of k needs to be set by the user of the algorithms. (Kang 2013) recently proposed a novel use of determinantal point processes for sampling the initial centroids for the KMEANS algorithm (we call it KMEANSD++). They, however, do not provide any evaluation establishing that KMEANSD++ is better than other algorithms. In this paper, we show that the performance of KMEANSD++ is comparable to KMEANS++ (both of which are better than KMEANSRAND) with KMEANSD++ having an additional that it can automatically approximate the value of k.

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arXiv2014

Semistochastic Quadratic Bound Methods

Partition functions arise in a variety of settings, including conditional random fields, logistic regression, and latent gaussian models. In this paper, we consider semistochastic quadratic bound (SQB) methods for maximum likelihood inference based on partition function optimization. Batch methods based on the quadratic bound were recently proposed for this class of problems, and performed favorably in comparison to state-of-the-art techniques. Semistochastic methods fall in between batch algorithms, which use all the data, and stochastic gradient type methods, which use small random selections at each iteration. We build semistochastic quadratic bound-based methods, and prove both global convergence (to a stationary point) under very weak assumptions, and linear convergence rate under stronger assumptions on the objective. To make the proposed methods faster and more stable, we consider inexact subproblem minimization and batch-size selection schemes. The efficacy of SQB methods is demonstrated via comparison with several state-of-the-art techniques on commonly used datasets.

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arXiv2013

Stochastic Bound Majorization

Recently a majorization method for optimizing partition functions of log-linear models was proposed alongside a novel quadratic variational upper-bound. In the batch setting, it outperformed state-of-the-art first- and second-order optimization methods on various learning tasks. We propose a stochastic version of this bound majorization method as well as a low-rank modification for high-dimensional data-sets. The resulting stochastic second-order method outperforms stochastic gradient descent (across variations and various tunings) both in terms of the number of iterations and computation time till convergence while finding a better quality parameter setting. The proposed method bridges first- and second-order stochastic optimization methods by maintaining a computational complexity that is linear in the data dimension and while exploiting second order information about the pseudo-global curvature of the objective function (as opposed to the local curvature in the Hessian).

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