204 research outputs found
Approximate resilience, monotonicity, and the complexity of agnostic learning
A function is -resilient if all its Fourier coefficients of degree at
most are zero, i.e., is uncorrelated with all low-degree parities. We
study the notion of of Boolean
functions, where we say that is -approximately -resilient if
is -close to a -valued -resilient function in
distance. We show that approximate resilience essentially characterizes the
complexity of agnostic learning of a concept class over the uniform
distribution. Roughly speaking, if all functions in a class are far from
being -resilient then can be learned agnostically in time and
conversely, if contains a function close to being -resilient then
agnostic learning of in the statistical query (SQ) framework of Kearns has
complexity of at least . This characterization is based on the
duality between approximation by degree- polynomials and
approximate -resilience that we establish. In particular, it implies that
approximation by low-degree polynomials, known to be sufficient for
agnostic learning over product distributions, is in fact necessary.
Focusing on monotone Boolean functions, we exhibit the existence of
near-optimal -approximately
-resilient monotone functions for all
. Prior to our work, it was conceivable even that every monotone
function is -far from any -resilient function. Furthermore, we
construct simple, explicit monotone functions based on and that are close to highly resilient functions. Our constructions are
based on a fairly general resilience analysis and amplification. These
structural results, together with the characterization, imply nearly optimal
lower bounds for agnostic learning of monotone juntas
Agnostic Learning of Disjunctions on Symmetric Distributions
We consider the problem of approximating and learning disjunctions (or
equivalently, conjunctions) on symmetric distributions over .
Symmetric distributions are distributions whose PDF is invariant under any
permutation of the variables. We give a simple proof that for every symmetric
distribution , there exists a set of
functions , such that for every disjunction , there is function
, expressible as a linear combination of functions in , such
that -approximates in distance on or
. This directly
gives an agnostic learning algorithm for disjunctions on symmetric
distributions that runs in time . The best known
previous bound is and follows from approximation of the
more general class of halfspaces (Wimmer, 2010). We also show that there exists
a symmetric distribution , such that the minimum degree of a
polynomial that -approximates the disjunction of all variables is
distance on is . Therefore the
learning result above cannot be achieved via -regression with a
polynomial basis used in most other agnostic learning algorithms.
Our technique also gives a simple proof that for any product distribution
and every disjunction , there exists a polynomial of
degree such that -approximates in
distance on . This was first proved by Blais et al.
(2008) via a more involved argument
Weighted Polynomial Approximations: Limits for Learning and Pseudorandomness
Polynomial approximations to boolean functions have led to many positive
results in computer science. In particular, polynomial approximations to the
sign function underly algorithms for agnostically learning halfspaces, as well
as pseudorandom generators for halfspaces. In this work, we investigate the
limits of these techniques by proving inapproximability results for the sign
function.
Firstly, the polynomial regression algorithm of Kalai et al. (SIAM J. Comput.
2008) shows that halfspaces can be learned with respect to log-concave
distributions on in the challenging agnostic learning model. The
power of this algorithm relies on the fact that under log-concave
distributions, halfspaces can be approximated arbitrarily well by low-degree
polynomials. We ask whether this technique can be extended beyond log-concave
distributions, and establish a negative result. We show that polynomials of any
degree cannot approximate the sign function to within arbitrarily low error for
a large class of non-log-concave distributions on the real line, including
those with densities proportional to .
Secondly, we investigate the derandomization of Chernoff-type concentration
inequalities. Chernoff-type tail bounds on sums of independent random variables
have pervasive applications in theoretical computer science. Schmidt et al.
(SIAM J. Discrete Math. 1995) showed that these inequalities can be established
for sums of random variables with only -wise independence,
for a tail probability of . We show that their results are tight up to
constant factors.
These results rely on techniques from weighted approximation theory, which
studies how well functions on the real line can be approximated by polynomials
under various distributions. We believe that these techniques will have further
applications in other areas of computer science.Comment: 22 page
Evaluating explainability for machine learning predictions using model-agnostic metrics
Rapid advancements in artificial intelligence (AI) technology have brought
about a plethora of new challenges in terms of governance and regulation. AI
systems are being integrated into various industries and sectors, creating a
demand from decision-makers to possess a comprehensive and nuanced
understanding of the capabilities and limitations of these systems. One
critical aspect of this demand is the ability to explain the results of machine
learning models, which is crucial to promoting transparency and trust in AI
systems, as well as fundamental in helping machine learning models to be
trained ethically. In this paper, we present novel metrics to quantify the
degree of which AI model predictions can be easily explainable by its features.
Our metrics summarize different aspects of explainability into scalars,
providing a more comprehensive understanding of model predictions and
facilitating communication between decision-makers and stakeholders, thereby
increasing the overall transparency and accountability of AI systems
Interpretable Machine Learning Model for Clinical Decision Making
Despite machine learning models being increasingly used in medical decision-making and meeting classification predictive accuracy standards, they remain untrusted black-boxes due to decision-makers\u27 lack of insight into their complex logic. Therefore, it is necessary to develop interpretable machine learning models that will engender trust in the knowledge they generate and contribute to clinical decision-makers intention to adopt them in the field.
The goal of this dissertation was to systematically investigate the applicability of interpretable model-agnostic methods to explain predictions of black-box machine learning models for medical decision-making. As proof of concept, this study addressed the problem of predicting the risk of emergency readmissions within 30 days of being discharged for heart failure patients. Using a benchmark data set, supervised classification models of differing complexity were trained to perform the prediction task. More specifically, Logistic Regression (LR), Random Forests (RF), Decision Trees (DT), and Gradient Boosting Machines (GBM) models were constructed using the Healthcare Cost and Utilization Project (HCUP) Nationwide Readmissions Database (NRD). The precision, recall, area under the ROC curve for each model were used to measure predictive accuracy. Local Interpretable Model-Agnostic Explanations (LIME) was used to generate explanations from the underlying trained models. LIME explanations were empirically evaluated using explanation stability and local fit (R2).
The results demonstrated that local explanations generated by LIME created better estimates for Decision Trees (DT) classifiers
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